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For more classes visit www.snaptutorial.com MATH 533 Week 1 Homework MATH 533 Week 1 Quiz MATH 533 Week 2 DQ 1 Case Let's Make a Deal MATH 533 Week 2 Homework (2 Sets) MATH 533 Week 2 Quiz MATH 533 Week 3 DQ 1 Ethics in Statistics Readings and Discussion

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- 1. MATH 533 Entire Course For more classes visit www.snaptutorial.com MATH 533 Week 1 Homework MATH 533 Week 1 Quiz MATH 533 Week 2 DQ 1 Case Let's Make a Deal MATH 533 Week 2 Homework (2 Sets) MATH 533 Week 2 Quiz MATH 533 Week 3 DQ 1 Ethics in Statistics Readings and Discussion MATH 533 Week 3 Homework MATH 533 Week 3 Quiz (2 Sets) MATH 533 Week 4 DQ 1 Case Statistics in Action: Medicare Fraud Investigations MATH 533 Week 4 Homework MATH 533 Week 4 Quiz (2 Sets) MATH 533 Week 5 DQ 1 Case Statistics in Action: Diary of a Kleenex User MATH 533 Week 5 Homework MATH 533 Week 5 Quiz MATH 533 Week 6 DQ 1 Case: Statistics in Action: Legal Advertising—Does It Pay? MATH 533 Week 6 Homework MATH 533 Week 6 Quiz MATH 533 Week 7 DQ 1 Case: Statistics in Action: Bid-Rigging in the Highway Construction Industry MATH 533 Week 7 Homework MATH 533 Week 7 Quiz MATH 533 Week 6 Course Project Part B Hypothesis Testing and Confidence Intervals (SALESCALL Project)
- 2. MATH 533 Week 7 Course Project Part C: Regression and Correlation Analysis (SALESCALL Project) MATH 533 Final Exam Set 1 MATH 533 Final Exam Set 2 ******************************************************* MATH 533 Final Exam Set 1 For more classes visit www.snaptutorial.com (TCO D) PuttingPeople2Work has a growing business placing out-of- work MBAs. They claim they can place a client in a job in their field in less than 36 weeks. You are given the following data from a sample. Sample size: 100 Population standard deviation: 5 Sample mean: 34.2 Formulate a hypothesis test to evaluate the claim. (Points : 10) Ans. b. H0 must always have equal sign, < 36 weeks 2. (TCO B) The Republican party is interested in studying the number of republicans that might vote in a particular congressional district. Assume that the number of voters is binomially distributed by party
- 3. affiliation (either republican or not republican). If 10 people show up at the polls, determine the following: Binomial distribution 3. (TCO A) Company ABC had sales per month as listed below. Using the Minitab output given, determine: (A) Range (5 points); (B) Median (5 points); and (C) The range of the data that would contain 68% of the results. (5 points). Raw data: sales/month (Millions of $) (TCO A) Company ABC had sales per month as listed below. Using the MegaStat output given, determine: (A) Range (5 points) (B) Median (5 points) (C) The range of the data that would contain 68% of the results. (5 points) 4. (TCO C, D) Tesla Motors needs to buy axles for their new car. They are considering using Chris Cross Manufacturing as a vendor. Tesla's requirement is that 95% of the axles are 100 cm ± 2 cm. The following data is from a test run from Chris Cross Manufacturing. Should Tesla select them as a vendor? Explain your answer. Descriptive statistics Tesla Motors needs to buy axles for their new car. They are considering using Chris Cross Manufacturing as a vendor. Tesla’s requirement is that 95% of the axles are 100 cm ± 5 cm. The following data is MegaStat output from a test run from Chris Cross Manufacturing. Descriptive statistics Question: Should Tesla select them as a vendor? Explain your answer. Answers (1) • Given that,
- 4. Tesla Motors needs to buy axles for their new car. They are considering using Chris Cross Manufacturing as a vendor. Tesla’s requirement is that 95% of the axles are 100 cm ± 5 cm. The following data is MegaStat output from a test run from Chris Cross Manufacturing: 5. (TCO D) A PC manufacturer claims that no more than 2% of their machines are defective. In a random sample of 100 machines, it is found that 4.5% are defective. The manufacturer claims this is a fluke of the sample. At a .02 level of significance, test the manufacturer's claim, and explain your answer. Final Page 2 1. (TCO B) The following table gives the number of visits to recreational facilities by kind and geographical region. (Points : 30) 2. (TCO B, F) The length of time Americans exercise each week is normally distributed with a mean of 15.8 minutes and a standard deviation of 2.2 minutes X P(X≤x) P(X≥x) Mean Std dev 11 .0146 .9854 15.8 2.2 15 .3581 .6419 15.8 2.2 21 .9910 .0090 15.8 2.2 24 .9999 .0001 15.8 2.2 p(lower) p(upper) ******************************************************* MATH 533 Final Exam Set 2
- 5. For more classes visit www.snaptutorial.com 1. (TCO A) Seventeen salespeople reported the following number of sales calls completed last month. 72 93 82 81 82 97 102 107 119 86 88 91 83 93 73 100 102 a. Compute the mean, median, mode, and standard deviation, Q1, Q3, Min, and Max for the above sample data on number of sales calls per month. b. In the context of this situation, interpret the Median, Q1, and Q3. (Points : 33) a. b. Median of the above sales calls means that if all the sales calls data points are arranged in an ascending order, then 91 Nos. of calls made would fall in the middle. So, there are as 8 sales calls 2. (TCO B) Cedar Home Furnishings has collected data on their customers in terms of whether they reside in an urban location or a suburban location, as well as rating the customers as either “good,” “borderline,” or “poor.” The data is below. Urban Suburban Total Good 60 168 228 Borderline 36 72 108 Poor 24 40 64 Total 120 280 400 If you choose a customer at random, then find the probability that the customer
- 6. a. is considered “borderline.” b. is considered “good” and resides in an urban location. c. is suburban, given that customer is considered “poor.” (Points : 18) 3. (TCO B) Historically, 70% of your customers at Rodale Emporium pay for their purchases using credit cards. In a sample of 20 customers, find the probability that a. exactly 14 customers will pay for their purchases using credit cards. b. at least 10 customers will pay for their purchases using credit cards. 4. (TCO B) The demand for gasoline at a local service station is normally distributed with a mean of 27,009 gallons per day and a standard deviation of 4,530 gallons per day. a. Find the probability that the demand for gasoline exceeds 22,000 gallons for a given day. c. How many gallons of gasoline should be on hand at the beginning of each day so that we can meet the demand 90% of the time (i.e., the station stands a 10% chance of running out of gasoline for that day)? (Points : 18) 5. (TCO C) An operations analyst from an airline company has been asked to develop a fairly accurate estimate of the mean refueling and baggage handling time at a foreign airport. A random sample of 36 refueling and baggage handling times yields the following results. Sample Size = 36
- 7. Sample Mean = 24.2 minutes Sample Standard Deviation = 4.2 minutes a. Compute the 90% confidence interval for the population mean refueling and baggage time. b. Interpret this interval. c. How many refueling and baggage handling times should be sampled so that we may construct a 90% confidence interval with a sampling error of .5 minutes for the population mean refueling and baggage time? (Points : 18) 6. (TCO C) The manufacturer of a certain brand of toothpaste claims that a high percentage of dentists recommend the use of their toothpaste. A random sample of 400 dentists results in 310 recommending their toothpaste. a. Compute the 99% confidence interval for the population proportion of dentists who recommend the use of this toothpaste. b. Interpret this confidence interval. c. How large a sample size will need to be selected if we wish to have a 99% confidence interval that is accurate to within 3%? (Points : 18) 7. (TCO D) A Ford Motor Company quality improvement team believes that its recently implemented defect reduction program has reduced the proportion of paint defects. Prior to the implementation of the program, the proportion of paint defects was .03 and had been stationary for the past 6 months. Ford selects a random sample of 2,000 cars built after the implementation of the defect reduction program. There were 45 cars with paint defects in that sample. Does the sample data provide evidence to conclude that the proportion of paint defects is now less than .03 (with a = .01)? Use the hypothesis testing procedure outlined below.
- 8. a. Formulate the null and alternative hypotheses. b. State the level of significance. c. Find the critical value (or values), and clearly show the rejection and nonrejection regions. d. Compute the test statistic. e. Decide whether you can reject Ho and accept Ha or not. f. Explain and interpret your conclusion in part e. What does this mean? g. Determine the observed p-value for the hypothesis test and interpret this value. What does this mean? h. Does the sample data provide evidence to conclude that the proportion of paint defects is now less than .03 (with a = .01)? (Points : 24) 8. (TCO D) A new car dealer calculates that the dealership must average more than 4.5% profit on sales of new cars. A random sample of 81 cars gives the following result. Sample Size = 81 Sample Mean = 4.97% Sample Standard Deviation = 1.8% Does the sample data provide evidence to conclude that the dealership averages more than 4.5% profit on sales of new cars (using a = .10)? Use the hypothesis testing procedure outlined below.
- 9. a. Formulate the null and alternative hypotheses. b. State the level of significance. c. Find the critical value (or values), and clearly show the rejection and nonrejection regions. d. Compute the test statistic. e. Decide whether you can reject Ho and accept Ha or not. f. Explain and interpret your conclusion in part e. What does this mean? g. Determine the observed p-value for the hypothesis test and interpret this value. What does this mean? h. Does the sample data provide evidence to conclude that the dealership averages more than 4.5% profit on sales of new cars (using a = .10)? (Points : 24) 1. (TCO E) Bill McFarland is a real estate broker who specializes in selling farmland in a large western state. Because Bill advises many of his clients about pricing their land, he is interested in developing a pricing formula of some type. He feels he could increase his business significantly if he could accurately determine the value of a farmer’s land. A geologist tells Bill that the soil and rock characteristics in most of the area that Bill sells do not vary much. Thus the price of land should depend greatly on acreage. Bill selects a sample of 30 plots recently sold. The data is found below (in Minitab), where X=Acreage and Y=Price ($1,000s). a. Analyze the above output to determine the regression equation. b. Find and interpret in the context of this problem.
- 10. c. Find and interpret the coefficient of determination (r-squared). d. Find and interpret coefficient of correlation. = .05) that the acreage can be used to predict the price? Test the utility of this model using a two-tailed test. Find the observed p-value and interpret.e. Does the data provide significant evidence ( f. Find the 95% confidence interval for mean price of plots of farmland that are 50 acres. Interpret this interval. g. Find the 95% prediction interval for the price of a single plot of farmland that is 50 acres. Interpret this interval. h. What can we say about the price for a plot of farmland that is 250 acres? (Points : 48) 4 1. (TCO E) An insurance firm wishes to study the relationship between driving experience (X1, in years), number of driving violations in the past three years (X2), and current monthly auto insurance premium (Y). A sample of 12 insured drivers is selected at random. The data is given below (in MINITAB): a. Analyze the above output to determine the multiple regression equation. b. Find and interpret the multiple index of determination (R-Sq).
- 11. = .05). Interpret your results.c. Perform the t-tests on and on (use two tailed test with ( d. Predict the monthly premium for an individual having 8 years of driving experience and 1 driving violation during the past 3 years. Use both a point estimate and the appropriate interval estimate. (Points : 31) ******************************************************* MATH 533 Week 1 Homework For more classes visit www.snaptutorial.com 1. Complete the table to the right. 2. In one university, language incorporated a 10-week extensive reading program to improve students’ Japanese reading comprehension. The professors collected 267 books originally written for Japanese children and required their students to read at least 40 of them as part of the grade in the course. The books were categorized into reading levels (color-coded for easy selection) according to length and complexity. Complete parts a through c. 3. Convert the relative frequency bar graph into a Pareto diagram. Interpret the graph. Choose the correct graph below. 4. Consider the stem-and-leaf display to the right.
- 12. 5. MINITAB was used to generate the histogram to the right. 6. Calculate the mean, median, and mode of the following data. 12 18 19 11 13 18 20 15 18 14 13 7. For one study, reasearchers sampled over 100,000 first-time candidates for the certified public account (CPA) exam and reached the total semester hours of college credit for each candidate. The mean and median for the data set were 146.73 and 153 hours, respectively. Interpret these values. Make a statement about the type of skewness, if any, that exists in the distribution of total semester hours. 8. Calculate the range, variance and standard deviation for the following sample. 3, 4, 2, 2, 6, 1, 6 9. Consider the data below on the number of carats for 8 diamonds. Complete parts a through d. 0.39 0.78 0.71 0.65 0.45 1.17 0.78 0.97 10. Compute the z-score corresponding to each of the values of x below. 11. A sample data set has a mean of 67 and a standard deviation of 15. Determine whether each of the following sample measurements are outliers. ******************************************************* MATH 533 Week 1 Quiz For more classes visit
- 13. www.snaptutorial.com 1. Graph the relative frequency histogram for the 300 measurements summarized in the relative frequency table to the right. 2. Would you expect the data sets that follow to possess relative frequency distributions that are symmetric, skewed to the right, or skewed to the left? Explain. Complete parts a through c below. 3. Consider the following sample of five measurements. 3, 4, 5, 2, 6 4. MINITAB was used to generate the histogram to the right. 5. A university’s language professors incorporated a 10-week extensive reading program into a second-semester Japanese language course in an effort to improve students’ Japanese reading comprehension. Fourteen students participated in this reading program. Complete parts a through c. 6. Calculate the mean for samples for which the sample size and ∑x are given below. ******************************************************* MATH 533 Week 2 DQ 1 Case Let's Make a Deal For more classes visit www.snaptutorial.com
- 14. A number of years ago, there was a popular television game show called Let's Make a Deal. The host, Monty Hall, would randomly select contestants from the audience and, as the title suggests, he would make deals for prizes. Contestants would be given relatively modest prizes and then would be offered the opportunity to risk that prize to win better ones. Suppose you are a contestant on this show. Monty has just given you a free trip worth $500 to a locale that is of little interest to you. He now offers you a trade: Give up the trip in exchange for a gamble. On the stage are three curtains, A, B, and C. Behind one of them is a brand-new car worth $45,000. Behind the other two curtains, the stage is empty. You decide to gamble and give up the trip. (The trip is no longer an option for you.) You must now select one of the curtains. Suppose you select Curtain A. In an attempt to make things more interesting, Monty then exposes an empty stage by opening Curtain C (he knows that there is nothing behind Curtain C). He then asks you if you want to keep Curtain A, or switch to Curtain B. What would you do? Hint: Questions to consider are: What is the probability of winning and the probability of losing the car prior to opening Curtain C? What is the probability of winning and the probability of losing the car after Curtain C is opened? What is your best strategy? ******************************************************* MATH 533 Week 2 Homework
- 15. For more classes visit www.snaptutorial.com 1. The table to the right gives a breakdown of 2,149 civil cases that were appealed. The outcome of the appeal, as well as the type of trial (judge or jury), was determined for each case. Suppose one of the cases is selected at random and the outcome of the appeal and type of trial are observed. 2. Zoologists investigated the likelihood of fallow deer bucks during the mating season. Researchers recorded 163 encounters between two bucks, one of which clearly initiated the encounter with the other. In these 163 initiated encounters, the zoologists kept track or not a physical contact fight occurred and whether the initiator ultimately won or lost the encounter. Suppose we select one of these 163 encounters and note the outcome (fight status and winner). Complete parts a through c. 3. Suppose 90% of kids who visit a doctor have a fever, and 10% of kids with a fever have sore throats. What’s the probability that a kid who goes to the doctor has a fever and a sore throat? 4. A table of classifying a sample of 78 patrons of a restaurant according to type of meal and their rating of the service is shown to the right. Suppose we select, at random, one of the 78 patrons. Given that the meal was dinner, what is the probability that the service was good? 5. The chance of winning a lottery game is 1 in approximately 26 million. Suppose you buy a $1 lottery ticket in anticipation of winning the $4 million grand prize. Calculate your expected net winnings for this single ticket. Interpret the result. 6. In a driver-side “star” scoring system for crash-testing new cars, each crash-tested car is given a rating from one star to five stars; the more stars in the rating the better is the level of crash protection in a head-on collision. A summary of the driver-side star ratings for 98 cars is reproduced in the accompanying table. Assume that 1 of 98
- 16. cars is selected at random, and let x equal the number of stars in the car’s driver-side star rating. Complete parts a through d. 7. If x is a binomial random variable, use the binomial probability table to find the probabilities below. 8. If x is a binomial random variable, calculate µ, , and for each of the following values of n and p. Complete parts a through f. 9. A country’s government has devoted considerable funding to missile defense research over the past 20 years. The latest development is the Space-Based Infrared System (SBIRS), which uses satellite imagery to detect and track missiles. The probability that an intruding object (e.g., a missile) will be detected on a flight track by SBIRS is 0.6. Consider a sample of 10 simulated tracks, each with an intruding object. Let x equal the number of these tracks where SBIRS detects the object. Complete parts a through d. 10. Many primary care doctors feel overworked and burdened by potential lawsuits. In fact, a group of researchers reported medicine as a career. Let x represent the number of sampled general practice physicians who do not recommend medicine as a career. Complete parts a through d. ******************************************************* MATH 533 Week 2 Quiz For more classes visit www.snaptutorial.com
- 17. 1. A country’s government has devoted considerable funding to missile defense research over the past 20 years. The latest development is the Space-Based Infrared System (SBIRS), which uses satellite imagery to detect and track missiles. The probability that an intruding object (e.g., a missile) will be detected on a flight track by SBIRS is 0.6. Consider a sample of 10 simulated tracks, each with an intruding object. Let x equal the number of these tracks where SBIRS detects the object. Complete parts a through d. 2. According to a consumer survey of young adults (18-24 years of age) who shop online, 18% own mobile phone with internet access. In a random sample of 200 young adults who shop online, let x be the numbers who own a mobile phone with internet access. 3. A table classifying a sample of 141 patrons of a restaurant according to type of meal and their rating of the service is shown to the right. Suppose we select, at random, one of the 141 patrons. Given that the meal was dinner, what is the probability that the service was good? 4. If x is a binomial random variable, use the binomial probability table to find the probabilities below. 5. The chances of a tax return being audited are about 17 in 1,000 if an income is less than $100,000 and 34 in 1,000 if an income is $100,000 or more. Complete parts a through e. 6. A national standard requires that public bridges over 20 feet in length must be inspected and rated every 2 years. The rating scale from 0 (poorest rating) to 9 (highest rating). A group of engineers used a probabilistic model to forecast the inspiration of all major bridges in a city. For the year 2020, the engineers forecast that 6% of all major bridges in that city will have ratings of 4 or below. Complete parts a and b. 7. Zoologists investigated the likelihood of fallow deer bucks fighting during the mating season. During a 270-hour observation period, the researchers recorded 205 encounters between two bucks. Of these, 161 involved one buck clearly initiating the encounter with the other. In these 161 initiated encounters, the zoologists kept track of whether or not a physical contact fight occurred and whether the initiator ultimately won or lost the encounter. (The buck that is driven away by the other is considered
- 18. the loser.) Suppose we select one of these 161 encounters and note the outcome (fight status and winter). 8. According to a certain golf association, the weight of the golf ball shall not be greater than 1,620 ounces (45.93 grams). The diameter of the ball shall not be less than 1.680 inches. The velocity of the ball shall not be greater than 250 feet per second. The golf association periodically checks the specifications of golf balls using random sampling. Five dozen of each kind are sampled, and if more than three do not meet size or velocity requirements, that kind of ball is removed from golf association’s approved list. Complete parts a and b. ******************************************************* MATH 533 Week 3 DQ 1 Ethics in Statistics Readings and Discussion For more classes visit www.snaptutorial.com 1. Why is it important to study ethics in statistics? Have you seen statistics misused? Without naming specific companies or people, can you provide examples? Please find (on the Internet or from the Keller library) and post an article regarding ethics and statistics. Please attach the article, or provide its link in your post, together with a brief summary of the
- 19. article in your own words. Be sure to use quotation marks around any words taken directly from the article (not to do so constitutes “plagiarism”). Then, in a separate post, review one or more articles posted by other students and provide the other student or students with your reflections (don’t just agree or disagree). ******************************************************* 2. MATH 533 Week 3 Homework For more classes visit www.snaptutorial.com 1. The mean gas mileage for a hybrid car is 56 miles per gallon. Suppose that the gasoline mileage is approximately normally distributed with a standard deviation of 3.3 miles per gallon. 2. The ages of a group of 50 women are approximately normally distributed with a mean of 49 years and a standard deviation of 5 years. One woman is randomly selected from the group, and her age is observed. 3. Resource Reservation Protocol (RSVP) was originally designed to establish signaling links for stationary networks. RSVP was applied to mobile wireless technology. A simulation study revealed that the transmission delay (measured in milliseconds) of an RSVP linked wireless device has an approximate normal distribution with mean µ = 49.5 milliseconds and milliseconds. Complete parts a and b.
- 20. 4. Almost all companies utilize some type of year-end performance review for their employees. Human Resources (HR) at a university’s Health Science Center provides guidelines for supervisors rating their subordinates. For example, raters are advised to examine for tendency to be either too lenient or too harsh. According to HR, “if you have this tendency, consider using a normal distribution—10% of employees (rated) exemplary, 20% distinguished, 40% competent, 20% marginal, and 10% unacceptable. “Suppose you are rating an employee’s performance on a scale of 1 (lowest) to 100 (highest). Also, assume the ratings follow a normal distribution with a mean of 49 and a standard deviation of 15. Complete parts a and b. 5. Personnel tests are designed to test a job applicant’s cognitive and/or physical abilities. A particular dexterity test is administered nationwide by a private testing service. It is known that for all tests administered last year, the distribution of scores was approximately normal with mean 78 and standard deviation 6.6. 6. Before negotiating a long-term construction contract, building contractors must carefully estimate the total cost of completing the project. At a certain university, a contractor proposed a model for total cost of a long-term contract based on the normal distribution. For one particular construction contract, the university assumed total cost, x, to be normally distributed with mean $860,000 and standard deviation $180,000.The revenue, R, promised to the contractor is $1,000,000. 7. The characteristics of an industrial filling process in which an expensive liquid is injected into a container was investigated. The quantity injected per container is approximately normally distributed with mean 10 units and standard deviation 0.02 units. Each unit of fill costs $10 per unit. If a container contains less than 10 units (that is, is underfilled), it must be reprocessed at a cost of $14. A property filled container sells for $125. Complete parts a through c. 8. A random sample of n = 100 observations is drawn from a population with mean equal to 46 and a standard deviation to 40. 9. A random sample of n = 64 observations is drawn from a population with a mean equal to 21 and a standard deviation equal to 16.
- 21. 10. The average salary for a certain profession is $74,500. Assume that the standard deviation of such salaries is $32,500. Consider a random sample of 52 people in this profession and let x represent the mean salary for the sample. 11. Some students paid a private tutor to help them their results on a certain mathematical test. These students had a mean change in score of +17 points, with a standard deviation of 69 points. In a random sample of 100 students who pay a private tutor to help them improve their results, what is the likelihood that change in the sample mean score is less than 10 points? ******************************************************* MATH 533 Week 3 Quiz For more classes visit www.snaptutorial.com 1. The average salary for a certain profession is $97,000. Assume that the standard deviation of such salaries is $33,500. Consider a random sample of 54 people in this profession and let x represent the mean salary for the sample. 2. Almost all companies utilize some type of year-end performance review for their employees. Human Resources (HR) at a university’s Health Science Center provides guidelines for supervisors rating their subordinates. For example, raters are advised to examine their ratings for a
- 22. tendency to be either too lenient or too harsh. According to HR, “if you have this tendency, consider using a normal distribution-----10% of employees (rated) exemplary, 20% distinguished, 40% competent, 20% marginal, and 10% unacceptable “Suppose you are rating an employee’s performance on a scale of 1 (lowest) to 100 (highest). Also, assume the ratings follow a normal distribution with a mean of 50 and a standard deviation of 16. Complete parts a and b. 3. Suppose a geyser has a mean time between eruptions of 60 minutes. If the interval of time between the eruptions is normally distributed with standard deviation 23 minutes, answer the following questions. 4. Assume the random variable X is normally distributed with mean µ = 50 and standard deviation . Complete the probability. Be sure to draw a normal curve with the area corresponding to the probability shaded. P(34 < X < 62) 5. The mean gas mileage for a hybrid car is 56 miles per gallon. Suppose that the gasoline mileage is approximately normally distributed with a standard deviation of 3.3 miles per gallon. ******************************************************* MATH 533 Week 4 DQ 1 Case Statistics in Action Medicare Fraud Investigations For more classes visit www.snaptutorial.com
- 23. Read the selection in your textbook pertaining to the Case: Statistics in Action: Medicare Fraud Investigations; load the data set for the case, MCFRAUD, into Minitab; answer the question about the case in the Discussion area; and likewise read and respond to the follow-on selections in the textbook for the case in the Statistics in Action Revisited. What is a point estimate of the mean overpayment? ******************************************************* MATH 533 Week 4 Homework For more classes visit www.snaptutorial.com 1. Health Care workers who use latex gloves with glove powder on a daily basis are particularly susceptible to developing a latex allergy. Each in a sample of 43 hospital employees who were diagnosed with a latex allergy based on a skin-prick test reported on their exposure to latex gloves. Summary statistics for the number of latex gloves used per week are x = 19.4 and s = 12.3. Complete parts (a) – (d). 2. The white wood material used for the roof of an ancient temple is imported from a certain country. The wooden roof must withstand as much as 100 centimeters of snow in the winter. Architects at a university conducted a study to estimate the mean bending strength of
- 24. the white wood roof. A sample of 25 pieces of the imported wood were tested and yielded the statistics x = 74.9 and s = 10.8 on breaking strength of the white wood with a 99% confidence interval. Interpret the result. 3. A group of researchers wants to estimate the true mean skidding distance along a new road in a certain forest. The skidding distances (in meters) were measured at 20 randomly selected road sites. These values are given in the accompanying table. Complete parts a through d. 4. In sociology, a personal network is defined as the people with whom you make frequent contact. A research program used a stratified random sample of men and women born between 1908 and 1937 to gauge the size of the personal network of older adults. Each adult in the sample was asked to “please name the people you have frequent contact with and who are also important to you.” Based on the number of people named, the personal network size for each adult was determined. The responses of 2,824 adults in this sample yielded statistics on network size, that is, the mean number of people named person was 14.3, with a standard deviation of 10.2. Complete parts a through c. 5. A newspaper reported that 50% of people say that some coffee shops are overpriced. The source of this information was a telephone survey of 40 adults. 6. A random sample of 1040 satellite radio subscribers was asked, “Do you have a satellite radio receiver in your car?” The survey found that 312 subscribes did, in fact, have a satellite receiver in their car. 7. In 2006, a survey of 400 adults in a region found that 45% had access to a high-speed Internet connection at home. 8. A gigantic warehouse stores approximately 80 million empty aluminum beer and soda cans. Recently, a fire occurred at the warehouse. The smoke from the fire contaminated many of the cans with black spot, rendering them unusable. A statistician was hired by the insurance company to estimate p, the true proportion of cans in the warehouse that were contaminated by their fire. How many aluminum cans should be randomly sampled to estimate p to within 0.08 with 90% confidence?
- 25. 9. According to an article the bottled water you are drinking may contain more bacteria and other potentially carcinogenic chemicals than are allowed by state and federal regulations. O the more than 1300 bottles studied, nearly one-third exceeded government levels. Suppose that a department wants an updated estimate of the population proportion of bottled water that violates at least one government standard. Determine the sample size (number of bottles) needed to estimate this proportion to within +/- 0.02 with 99% confidence. A company tests all new brands of golf balls to ensure that they meet certain specifications. One test conducted is intended to measure the average distance traveled when the ball is hit by a machine. Suppose the company wishes to estimate the mean distance for a new brand within 1.2 yards with 90% confidence. Assume that past tests have indicated that the standard deviation of the distances the machine hits golf balls is approximately 10 yards. How many golf balls should be hit by the machine to achieve the desired accuracy in estimating the mean? ******************************************************* MATH 533 Week 4 Quiz For more classes visit www.snaptutorial.com
- 26. 1. A random samples of 1020 satellite radio subscribers were asked, “Do you have a satellite radio receiver in your car?” The survey found that 102 subscribers did, in fact, have a satellite receiver in their car. 2. Each child in a sample of 64 low-income children was administered a language and communication exam. The sentence complexity scores had a mean of 7.62 and a standard deviation of 8.91. Complete parts a through d. 3. In a sample of 60 stores of a certain company, 50 violated a scanner accuracy standard. It has been demonstrated that the conditions for a valid large-sample confidence interval for the true proportion of the stores that violate the standard were not met. Determine the number of stores that must be sampled in order to estimate the true proportion to within 0.05 with 95% confidence using the large-sample method. 4. A company wants to test a randomly selected sample of n water specimens and estimate the mean daily rate of pollution produced by a mining operation. If the company wants a 90% confidence interval estimate with a sampling error of 1.8 milligrams per liter (mg/L), how many water specimens are required in the sample? Assume prior knowledge indicates that pollution readings in water samples taken during a day are approximately normally distributed with a standard deviation equal to 8 mg/L. 5. The white wood material used for the roof of an ancient temple is imported from a certain country. The wooden roof must withstand as much as 100 centimeters of snow in the winter. Architects at a university conducted a study to estimate the mean bending strength of the white roof. A sample of 25 pieces of the imported wood were tested and yielded the statistics x = 74.5 and s = 10.3 on breaking strength (MPa). Estimate the true mean breaking strength of the white wood with a 99% confidence interval. Interpret the result. *******************************************************
- 27. MATH 533 Week 5 DQ 1 Case Statistics in Action: Diary of a Kleenex User For more classes visit www.snaptutorial.com Read the selection in your text book pertaining to the Case: Statistics in Action: Diary of a Kleenex® User; load the data set for the case, TISSUES, into Minitab; answer the question about the case in the Discussion area; and likewise read and respond to the follow-on selections in the textbook for the case in the Statistics in Action Revisited. How would you briefly summarize the case, and the data that was generated? ******************************************************* MATH 533 Week 5 Homework For more classes visit www.snaptutorial.com
- 28. 1. A study of n = 90,000 first-time candidates for an exam found that the number of semester hours of college credit taken by the sampled candidates is summarized by x = 145.72 and s = 18.53. A professor claims that the true mean number of semester hours of college credit taken is 145. 2. A study of n = 59 hospital employees found that the number of latex gloves used per week by the sampled worker is summarized by x = 21.2 and s = 13.1. Let µ represent the mean number of latex gloves used per week by all hospital employees. Consider testing 3. The final scores of games of a certain sport were compared against the final point spreads established by oddsmakers. The difference between the game outcome and point spread (called a point-spread error) was calculated for 255 games. The sample mean and sample standard deviation of the point-spread errors are x = 1.3 and s = 12.9. Use this information to test the hypothesis that the true mean point-spread error for all games is larger than 0. Conduct the test at and interpret the result. 4. For the and observed significance level (p-value) pair, indicate whether the null hypothesis would be rejected. , p-value = 0.05 5. Consider a test of performed with the computer. The software reports a two-tailed p-value of 0.1032. Make the appropriate conclusion for each of the following situations. 6. When bonding teeth, orthodonists must maintain a dry filed. A new bonding adhesive has been developed to eliminate the neccessity of a try field. However, there is concern that the new bonding adhesive is not as strong as the current standard, a composite adhesive. Tests on a sample of 12 extracted teeth bonded with the new adhesive resulted in a mean breaking srength (after 24 hours) of x = 5.83 Mpa and a standard deviation of s = 0.49 Mpa. Orthodontists want to know if the true mean breaking strength is less than 6.46 Mpa, the mean braking strength of the composite adhesive. 7. Whether planning for a new forest road to be used for tree harvesting, Planners must select the location to minimize tractor skidding distance. The skidding distances (in meters) were measured
- 29. at 20 randomly selected road sites. The data are given below. A logger working on the road claims the mean skidding distance is atleast 418 meters. Is there sufficient evidence to refute this claim? Use α = 0.10. 8. Suppose 47 0f 110 randomly selected shoppers believe that “Made in the USA” means that 100% of labor and materials are from the United States. Let p represent the true proportion of consumers who believe “Made in the USA” means 100% of labor and materials are from the United States. Complete parts a through e. 9. The National Institute for Standards and Technology (NIST) mandates that for every 100 items scanned through the electronic checkout scanner at a retail store, no more than two should have an inaccurate price. A study of random items purchased at different California stores found that 3.3% had the wrong price. Assume that the study inclluded 841 randomly selected items. Complete parts a through e. 10. Suppose a consumer group rated 44 brands of toothpaste based on whether or not the brand an American Dental Association (ADA) seal verifying effective decay prevention. The results of a hypothesis test for the proportion of brands with the seal to the right. Complete parts a through c. ******************************************************* MATH 533 Week 5 Quiz For more classes visit www.snaptutorial.com
- 30. 1. A group of professors investigated first-year college students’ knowledge of astronomy. One concept of interest was the Big Bang Theory of the creation of the universe. In a sample 0f 141 freshman students, 35 believed that the Big Bang Theory accurately described the creation of plantery systems. Baesd on this information, is it correct at the α = 0.01 level of significance to state that more than 20% of all freshman college students believe the Big Bang theory describes the creation of planetary systems? 2. A study was conducted to evaluate the effectiveness of a new mosquito repellent designed by the U.S. Army to be applied as camouflage face paint. The repellent was applied to the forearms of 5 volunteers who then were exposed to 15 active mosquitos for a 10- hour period. The percentage of the forearm surface area protected from bites (called percent repellency) was calculated for each of the five volunteers. For one color of paint (loam), the following summary statistics were obtained: x =83%, s = 14%. Complete parts a and b. 3. A study of n = 110,000 first-time candidates for an exam found that the number of semester hours of college credit taken by the sampled candidate is summarized by x = 146.78 and s = 20.44. A professor claims that the true mean number of semester hours of college credit taken is 146. 4. Suppose 36 0f 104 randomly selected shoppers believe that “Made in the USA” means that 100% of labor and materials are from the United States. Let p represent the true proportion of consumers who believe “Made in the USA” means 100% of labor and materials are from the United States. Complete parts a through e. 5. The final scores of games of a certain sport were compared against the final point spreads establiished by oddmakers. The difference between the game outcome and point spread (called a point-spread error) was calculated for 240 games. The sample mean and sample standard deviation of the point-spread errors are x = 1.7 and s = 14.6. Use this information to test the hypothesis that the true mean point-spread error for all games is lareger than 0. Conduct the test at α = 0.05 and interpret the result.
- 31. ******************************************************* MATH 533 Week 6 Course Project Part B Hypothesis Testing and Confidence Intervals (SALESCALL Project) For more classes visit www.snaptutorial.com Your Instructor will provide you with four manager speculations, a.- d., in the Doc Sharing file. 1. Using the sample data, perform the hypothesis test for each of the above situations in order to see if there is evidence to support your manager’s belief in each case a.-d. In each case use the Seven Elements of a Test of Hypothesis, in Section 6.2 of your text book, using the α provided by your Instructor in the Doc Sharing materials, and explain your conclusion in simple terms. Also be sure to compute the p-value and interpret. 2. Follow this up with computing confidence intervals (the required confidence level will be provided by your Instructor) for each of the variables described in a.-d., and again interpreting these intervals. 3. Write a report to your manager about the results, distilling down the results in a way that would be understandable to someone who does not know statistics. Clear explanations and interpretations are critical. 4. All DeVry University policies are in effect, including the plagiarism policy.
- 32. 5. Project Part B report is due by the end of Week 6. 6. Project Part B is worth 100 total points. See grading rubric below. Submission: The report from part 3 + all of the relevant work done in the hypothesis testing (including Minitab) in 1., and the confidence intervals (Minitab) in 2. as an appendix. ******************************************************* MATH 533 Week 6 DQ 1 Case: Statistics in Action: Legal Advertising—Does It Pay For more classes visit www.snaptutorial.com Read the Case: Statistics In Action: Legal Advertising—Does It Pay?, and answer the following questions. (The case is included in your textbook, Chapter 10.) The data set for the case study is LEGALADV, and it is available in your textbook resources, so you don't have to enter the data! Summarize what the case is about, and what the variables represent. *******************************************************
- 33. MATH 533 Week 6 Homework For more classes visit www.snaptutorial.com 1. A MINITAB printout relating the size of the diamond (number of carats) to the asking price (dollars) for 308 diamonds is shown below. Complete parts a through e. 2. The average driving distance (yards) and driving accuracy (percent of drives that land in the fairway) for 8 golfers are recorded in the table to the right. Complete parts a through e below. 3. Many entrepreneurs have donated money to various causes. Data on the total amount pledged and remaining net worth for the 10 top donors are given in the table. Complete parts a through d. 4. A magazine reported the average charge and the averege length of hospital stay for patients in a sample of 7 regions. The printout is shown below. Complete parts a through e. 5. Adult male rhesus monkeys were exposed to a visual stimulus ( panel of light-emitting diodes), and their eye, head, and body movements were electronically recorded. In on variation of the experiment, two variables were measured, active head movement (x, percent per degree) and body-plus-rotation (y,percent per degree). The data for n = 37 trails were subjected to a simple linear regression analysis, with = 0.23. Complete parts a through c. 6. If you pay more in tuition to go to a top business school, will it necessarily result in a higher probability of a job offer at graduation? Let y = percentage of graduates with job offers and x = tuition cost; then fit the simple linear model, E(y) = + x, to the data below. Is
- 34. there sufficient evidence (at α = 0.10) of a positive linear relationship between y and x? 7. Banks in a state have been charged with withdrawing from urban areas with a high percentage of minorities. To examine this charge, a study compiled county by county data on the number (y) of people in each county per branch bank in the county and the percentage (x) of the population in each county that is minority. Complete parts a through c. 8. The rank of the top 10 billionaires, their net worth (y), and their ages (x) are given in the table to the right. Complete parts a through d below. 9. A group of researchers developed a new method for ranking the total driving performance of golfers on a tour. The method requires knowing a golfer’s averaging driving distance (yards) and driving accuracy (percent of drives that land in the fairway). They construct a straight-line model relating driving accuracy(y) to driving distance(x). A MINITAB printout with prediction and confidence intervals for a driving distance of x = 300 is shown below. 10. The accompanying data in the table below were derived from life tests for two different brands of cutting tools. Complete parts a through c. ******************************************************* MATH 533 Week 6 Quiz For more classes visit www.snaptutorial.com
- 35. 1. An association was formed by students to protest labor exploitation in the apparel industry. There were 18 student “sit-ins” for a “sweet-free campus” organized at several universities. Data were collected for the duration (in days) of each sit-in, as well as the number of student arrests. The data for 5 sit-ins in which there was at least one arrest and the results of a simple linear regression are found below. Let y be the number of arrests and x be the duration. Complete parts a through d. 2. A group of researchers developed a new method for ranking the total driving performance of golfers on a tour. The main average driving distance (yards) and driving accuracy (percent of drives that land in the fairway). They construct a standard accuracy (y) to driving distance (x). A MINITAB printout with prediction and confidence intervals for a driving distance. 3. Many entrepreneurs have donated money to various causes. Data on the total amount pledged and remaining net worth for the 10 top donors are given in the table. Complete parts a through d. 4. The quality of the orange juice produced by a manufacturer is constantly monitored. There are numerous sensory and chemical components that combine to make the best-tasting orange juice. For example, one manufacturer has developed a quantitative index of the “sweetness” of orange juice. Suppose a manufacturer wants to use simple linear regression to predict the sweetness (y) from the amount of pectin(x). Find a 90% confidence interval for the true slope of the line. Interpret the result. 5. A study of the effect of massage on boxing performance measured a boxer’s lactate concentration (in mM) and perceived recovery (on a 28-point scale). On the basis of the information provided by the study, the data shown in the accompanying table were obtained for 16 five-round boxing performances in which a massage was given to the boxer between rounds. Conduct a test to determine whether blood lactate level(y) is linearly related to the perceived recovery (x). Use α = 0.10.
- 36. 6. A MINITAB printout relating the size of the diamond (number of carats) to the asking price (dollars) is shown below. Complete parts a through e. ******************************************************* MATH 533 Week 7 Course Project Part C: Regression and Correlation Analysis (SALESCALL Project) For more classes visit www.snaptutorial.com Your Instructor will specify for you the dependent variable and the independent variables in your Case and data. Using MINITAB perform the regression and correlation analysis for the data by answering the following. 1. Generate a scatterplot for the specified dependent variable and the specified independent variable, including the graph of the "best fit" line. Interpret. 2. Determine the equation of the "best fit" line, which describes the relationship between the dependent variable and the selected independent variable. 3. Determine the coefficient of correlation. Interpret. 4. Determine the coefficient of determination. Interpret.
- 37. 5. Test the utility of this regression model (use a two tail test with the α provided by your Instructor). Interpret your results, including the p-value. 6. Based on your findings in 1-5, what is your opinion about using the designated independent variable to predict the designated dependent variable? Explain. 7. Compute the confidence interval for beta-1 (the population slope), using the confidence level specified by your Instructor. Interpret this interval. 8. Using an interval, estimate the average for the dependent variable for a selected value of the independent variable (to be provided by your Instructor). Interpret this interval. 9. Using an interval, predict the particular value of the dependent variable for a selected value of the independent variable (to be provided by your Instructor). Interpret this interval. 10. What can we say about the value of the dependent variable for values of the independent variable that are outside the range of the sample values? Explain your answer. In an attempt to improve the model, we will attempt to do a multiple regression model predicting the dependent variable based on all of the independent variables. 11. Using MINITAB run the multiple regression analysis using the designated dependent and independent variables. State the equation for this multiple regression model. 12. Perform the Global Test for Utility (F-Test). Explain your conclusion. 13. Perform the t-test on each independent variable. Explain your conclusions and clearly state how you should proceed. In particular, which independent variables should we keep and which should be discarded. If any independent variables are to be discarded, re-run the multiple regression, including only the significant independent variables, and include the final Minitab output, with interpretation. 14. Is this multiple regression model better than the linear model that we generated in parts 1-10? Explain.
- 38. 15. All DeVry University policies are in effect, including the plagiarism policy. 16. Project Part C report is due by the end of Week 7. 17. Project Part C is worth 100 total points. See grading rubric below. Summarize your results from 1-14 in a report that is three pages or less in length and explains and interprets the results in ways that are understandable to someone who does not know statistics. Submission: The summary report + all of the work done in 1-14 (Minitab Output + interpretations) as an appendix. ******************************************************* MATH 533 Week 7 DQ 1 Case: Statistics in Action: Bid-Rigging in the Highway Construction Industry For more classes visit www.snaptutorial.com Read the Case: Statistics in Action: Bid-Rigging in the Highway Construction Industry, in Chapter 11 of your textbook, and answer the following questions. The data set, FLAG, for the case study is available in the publisher’s website, so you don’t need to enter the data into Minitab by hand.
- 39. What is this case about? Describe the key variables. ******************************************************* MATH 533 Week 7 Homework For more classes visit www.snaptutorial.com 1. Researchers developed a safety performance function (SPF), which estimates the probability of occurrence of a crash for a given segment of roadway. Using data on over 100 segments of roadway, they fit the model E(y) = + + , where y = number of crashes per three years, = roadway length (miles), and = average annual daily traffic (number of vehicles) = AADT. 2. The data shown below represent the annual earnings (y), age ( , and hours worked per day (x2) for a random sample of street vendors in a certain. Complete parts a through f. 3. Data on the average annual precipitation (y), altitude (x1), latitude (x2), and distance from the coast (x3) for a particular state were collected for 10 meteorological stations. The observations are listed in the table below. Consider the first-order model y = + + , + ε. Complete parts a through c. 4. A manufacturer of boiler drums wants to use regression to predict the number of hours needed to erect the drums in future projects. To accomplish this task, data on 15 boilers were collected. In addition to hours (y), the variables measured were boiler capacity (x1 = 1b/hr), boiler design pressure (x2 = pounds per square inch, or psi), boiler type (x3 = 1 if industry field erected, 0 if utility filed
- 40. erected), drum type (x4 = 1 if steam, 0 if mud). Complete parts a through d. 5. A magazine reported on a study of the reliability of a commercial kit to test for arsenic in groundwater. The field kit was used to test a sample of 20 ground water wells in a country. In addition to the arsenic level (micrograms per liter), the latitude (degrees), and depth (feet) of each well was measured. Complete parts a through g. 6. A researcher wants to find a model that relates square footage x1, number of bedrooms x2, number of baths x3, and asking price y (in thousands of dollars) of a house. Complete parts (a) through (h). ******************************************************* MATH 533 Week 7 Quiz For more classes visit www.snaptutorial.com 1. Data on the average annual precipitation (y), altitude (x1), latitude (x2), and distance from the coast (x3) for a particular state were collected for 10 meteorological stations. The observations are listed in the table below. Consider the first-order model y = + + , + ε. Complete parts a through c. 2. Researchers developed a safety performance function (SPF), which estimates the probability of occurrence of a crash for a given segment of roadway. Using data on over 100 segments of roadway, they fit the model E(y) = + + , where y = number of crashes
- 41. per three years, x1 = roadway length (miles), and x2 = average annual daily traffic (number of vehicles) = AADT. 3. The data shown below represent the annual earnings (y), age (x1), and hours worked per day (x2) for a random sample of street vendors in a certain city. Complete parts a through f. 4. A manufacturer of boiler drums wants to use regression to predict the number of hours needed to erect the drums in future projects. To accomplish this task, data on 15 boilers were collected. In addition to hours (y), the variables measured were boiler capacity (x1 = 1b/hr), boiler design pressure (x2 = pounds per square inch, or psi), boiler type (x3 = 1 if industry field erected, 0 if utility filed erected), drum type (x4 = 1 if steam, 0 if mud). Complete parts a through d. *******************************************************