# Confidence Intervals for the Mean1.Assume that a sample is use.docx

15 de Nov de 2022
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### Confidence Intervals for the Mean1.Assume that a sample is use.docx

• 1. Confidence Intervals for the Mean 1.Assume that a sample is used to estimate a population mean μμ. Find the margin of error M.E. that corresponds to a sample of size 11 with a mean of 30.3 and a standard deviation of 13.8 at a confidence level of 99.5%. Report ME accurate to one decimal place because the sample statistics are presented with this accuracy. M.E. = Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places. 2.The effectiveness of a blood-pressure drug is being investigated. An experimenter finds that, on average, the reduction in systolic blood pressure is 19.8 for a sample of size 906 and standard deviation 19.6. Estimate how much the drug will lower a typical patient's systolic blood pressure (using a 95% confidence level). Enter your answer as a tri-linear inequality accurate to one decimal place (because the sample statistics are reported accurate to one decimal place). < μ < Answer should be obtained without any preliminary rounding. 3.You must estimate the mean temperature (in degrees Fahrenheit) with the following sample temperatures:
• 2. 62.3 39.4 56.7 57.7 63.5 65.5 53.9 67.7 63.1 56.5 61.7 59.7 Find the 98% confidence interval. Enter your answer as an open-interval (i.e., parentheses) accurate to two decimal places (because the sample data are reported accurate to one decimal place). 98% C.I. = Answer should be obtained without any preliminary rounding. 4.SAT scores are distributed with a mean of 1,500 and a standard deviation of 300. You are interested in estimating the average SAT score of first year students at your college. If you would like to limit the margin of error of your 95% confidence interval to 25 points, how many students should you sample? Make sure to give a whole number answer. 5.For a confidence level of 99% with a sample size of 21, find the critical t value. For Question #5 when you are asked to use find the t-value corresponding to a certain confidence level and degrees of
• 3. freedom use this link: http://www.usablestats.com/calcs/tinv Remember that we are only calculating Confidence Intervals using t! 6.If n=26, ¯xx¯(x-bar)=31, and s=4, find the margin of error at a 95% confidence level Give your answer to two decimal places. 7.Assume that a sample is used to estimate a population mean μμ. Find the margin of error M.E. that corresponds to a sample of size 13 with a mean of 64.5 and a standard deviation of 17.9 at a confidence level of 95%. Report ME accurate to one decimal place because the sample statistics are presented with this accuracy. M.E. = Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places. THIS LINKS MIGHT BE USEFUL: http://onlinestatbook.com/2/estimation/intro.html http://onlinestatbook.com/2/estimation/characteristics.html http://onlinestatbook.com/2/estimation/confidence.html http://onlinestatbook.com/2/estimation/mean.html http://onlinestatbook.com/2/estimation/t_distribution.html https://www.learner.org/courses/againstallodds/unitpages/unit26 .html https://www.youtube.com/watch?v=MuIir6rGNN0&feature=yout u.be
• 5. Round final answer to one decimal place 4.Giving a test to a group of students, the grades and gender are summarized below A B C Total Male 13 6 9 28 Female 7 16 5 28 Total 20 22 14 56 Let ππ represent the percentage of all male students who would receive a grade of B on this test. Use a 90% confidence interval to estimate p to three decimal places. Enter your answer as a tri-linear inequality using decimals (not percents). < p <
• 6. 5.You want to obtain a sample to estimate a population proportion. At this point in time, you have no reasonable estimate for the population proportion. You would like to be 98% confident that you esimate is within 0.5% of the true population proportion. How large of a sample size is required? n = Do not round mid-calculation. However, use a critical value accurate to three decimal places. 6.A political candidate has asked you to conduct a poll to determine what percentage of people support her. If the candidate only wants a 10% margin of error at a 95% confidence level, what size of sample is needed? Give your answer in whole people. 7.If n=310 and ˆpp^ (p-hat) =0.22, find the margin of error at a 95% confidence level Give your answer to three decimals 8.Out of 600 people sampled, 450 had kids. Based on this, construct a 95% confidence interval for the true population proportion of people with kids.
• 7. Give your answers as decimals, to three places < p < 9.Express the confidence interval (67.5%,74.3%)(67.5%,74.3%) in the form of ˆp±MEp^±ME. % ± % 10.Express the confidence interval 61.7%<p<77.3%61.7%<p<77.3% in the form of ˆp±MEp^±ME. % ±± % You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately p∗ =72%p∗ =72%. You would like to be 90% confident that your estimate is within 3% of the true population proportion. How large of a sample size is required? n = Do not round mid-calculation. However, use a critical value accurate to three decimal places. THIS LINKS MIGHT BE USEFUL: https://www.youtube.com/watch?v=3ReWri_jh3M&feature=yout u.be https://www.youtube.com/watch?v=FCxPxAWToJk&feature=yo utu.be
• 8. https://ohm-website- data.s3.amazonaws.com/cfiles/2408/ModelCIProp.pdf https://ohm-website- data.s3.amazonaws.com/cfiles/2408/ReadingE10.pdf OTHER QUESTIONS 1.We wish to estimate what percent of adult residents in a certain county are parents. Out of 500 adult residents sampled, 355 had kids. Based on this, construct a 95% confidence interval for the proportion, p, of adult residents who are parents in this county. Give your answers as decimals, to three places. < p < 2. Giving a test to a group of students, the grades and gender are summarized below A B C Total Male 12 7 9 28 Female 16 19 11 46 Total
• 9. 28 26 20 74 Let ππ represent the percentage of all male students who would receive a grade of A on this test. Use a 98% confidence interval to estimate p to three decimal places. Enter your answer as a tri-linear inequality using decimals (not percents). < p < 3. If n=340 and ˆpp^ (p-hat) =0.69, find the margin of error at a 90% confidence level Give your answer to three decimals 4.You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately p∗ =58%p∗ =58%. You would like to be 99.9% confident that your esimate is within 5% of the true population proportion. How large of a sample size is required? n =
• 10. Do not round mid-calculation. However, use a critical value accurate to three decimal places. 5.For a confidence level of 98% with a sample size of 17, find the critical t value. 6.If n=20, ¯xx¯(x-bar)=34, and s=4, find the margin of error at a 95% confidence level Give your answer to two decimal places. 7.Karen wants to advertise how many chocolate chips are in each Big Chip cookie at her bakery. She randomly selects a sample of 52 cookies and finds that the number of chocolate chips per cookie in the sample has a mean of 16.8 and a standard deviation of 2.6. What is the 80% confidence interval for the number of chocolate chips per cookie for Big Chip cookies? Enter your answers accurate to one decimal place (because the sample statistics are reported accurate to one decimal place). < μ <