# Week 3 – Multiple Choice4) A random sample of 100 observations f.docx

10 de Nov de 2022
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### Week 3 – Multiple Choice4) A random sample of 100 observations f.docx

• 1. Week 3 – Multiple Choice 4) A random sample of 100 observations from a population with standard deviation 60 yielded a sample mean of 111. Complete parts a through c. a) Test the null hypothesis that μ=100 against the alternative hypothesis that μ>100, using α=0.05. Interpret the results of the test. ⃝ Hₒ is not rejected ⃝ Hₒ is rejected Interpret the results of the test. Choose the correct interpretation below: ⃝ There is sufficient evidence to indicate the true population mean is not equal to 100 at α=0.05 ⃝ There is sufficient evidence to indicate the true population mean is greater than 100 at α=0.05 ⃝ There is sufficient evidence to indicate the true population mean is smaller than 100 at α=0.05 b) Test the null hypothesis that μ=100 against the alternative hypothesis that μ≠100, using α=0.05. Interpret the results of the test. ⃝ Hₒ is not rejected ⃝ Hₒ is rejected Interpret the results of the test. Choose the correct interpretation below: ⃝ There is insufficient evidence to indicate μ is smaller than 100 at α=0.05 ⃝ There is insufficient evidence to indicate μ is not equal to 100 at α=0.05 ⃝ There is insufficient evidence to indicate μ is greater than 100 at α=0.05 c) Compare the results of the two test you conducted. Explain
• 2. why the results differ. Choose the correct answer below. ⃝ The results differ because the alternative hypothesis in part a is more specific than the one in b ⃝ The results do not differ because these two tests are equivalent ⃝ The results differ because the alternative hypothesis in part b is more specific than the one in a 5) The final scores of games of a certain sport were compared against the final point spreads established by oddmakers. The difference between the game outcome and point spread (called point-spread error) was calculated for 260 games. The mean and standard deviation of the point-spread errors are x=1.2 and s=11.4. Use this information to test the hypothesis that the true mean point-spread error for all games differs from 0. Conduct the test α=0.05 and interpret the result. What is the appropriate conclusion at α=0.05? ⃝ A. Reject Hₒ. There is insufficient evidence to indicate that μ≠0 ⃝ B. Do not reject Hₒ. There is sufficient evidence to indicate that μ≠0 ⃝ C. Do not reject Hₒ. There is insufficient evidence to indicate that μ≠0 ⃝ D. Reject Hₒ. There is sufficient evidence to indicate that μ≠0 6) If a hypothesis test were conducted using α=0.01, for which of the following p-values would the null hypothesis be rejected? a. 0.009 b. 0.02 a) What is the conclusion for a p-value of 0.009? ⃝ A. Reject the null hypothesis since the p-value is not less than the value α ⃝ B. Do not reject the null hypothesis since the p-value is less than the value α ⃝ C. Do not reject the null hypothesis since the p-value is not less than the value α ⃝ D. Reject the null hypothesis since the p-value is less than the value α b) What is the conclusion for a p-value of 0.02?
• 3. ⃝ A. Do not reject the null hypothesis since the p-value is not less than the value α ⃝ B. Do not reject the null hypothesis since the p-value is less than the value α ⃝ C. Reject the null hypothesis since the p-value is less than the value α ⃝ D. Reject the null hypothesis since the p-value is not less than the value α 7) For the α and observed significance level (p-value) pair, indicate whether the null hypothesis would be rejected. Α=0.01 p-value=0.45 Choose the correct conclusion below. ⃝ A. Do not reject the null hypothesis since the p-value is not less than the value α ⃝ B. Reject the null hypothesis since the p-value is not less than the value α ⃝ C. Reject the null hypothesis since the p-value is less than the value α ⃝ D. Do not reject the null hypothesis since the p-value is less than the value α 8) In a test of the hypothesis Hₒ: μ=10 versus μ≠10, a sample of n=40 observations possessed mean x=10.7 and standard deviation s=2.6. Find the p-value is p= _____________ (Round to four decimal places as needed) 9) In a study it was found that the average age of cable TV shoppers was 54 years. Suppose you want to test the null hypothesis, Hₒ: μ=154, using a sample of n=80 cable TV shoppers. a) Find the p-value of a two-tailed test if x=55.1 and s=10.1 (Round to four decimal places as needed) b) Find the p=value of an upper-tailed test if x=55.1 and s=10.1(Round to four decimal places as needed) 10) A sample of six measurements, randomly selected from a normally distributed population, resulted in the summary statistics x=5.6 and s=1.2. Complete parts a through c a) Test the null hypotheis that the mean of the population is 7
• 4. against the alternative hypothesis, μ<7. Use α=0.05. ⃝ A. Do not reject Hₒ. There is sufficient evidence to indicate that μ<7 ⃝ B. Reject Hₒ. There is sufficient evidence to indicate that μ<7 ⃝ C. Do not reject Hₒ. There is insufficient evidence to indicate that μ<7 ⃝ D. Reject Hₒ. There is insufficient evidence to indicate that μ<7 Test the null hypothesis that the mean of the population is 7 against the alternative hypothesis μ≠7. Use α=0.05. ⃝ A. Reject Hₒ. There is insufficient evidence to indicate that μ≠7 ⃝ B. Do not reject Hₒ. There is sufficient evidence to indicate that μ≠7 ⃝ D. Reject Hₒ. There is sufficient evidence to indicate that μ≠7 ⃝ C. Do not reject Hₒ. There is insufficient evidence to indicate that μ≠7 c)Find the observed significance level for each test. Choose the correct significance level for part a below ⃝ A. p-value<0.0005 ⃝ B. 0.050<p-value<0.100 ⃝ D. 0.005<p-value<0.001 ⃝ C. 0.005<p-value<0.010 ⃝ E. 0.010<p-value<0.025 ⃝ F. 0.001<p-value<0.005 Choose the correct significance level for part b below ⃝ A. 0.050<p-value<0.100 ⃝ B. 0.100<p-value<0.200 ⃝ D. p-value<0.001 ⃝ C. 0.001<p-value<0.002 ⃝ E. 0.020<p-value<0.050 ⃝ F. 0.002<p-value<0.010
• 5. 11) Info below a) Do the data indicate that the true mean number of suicide bombings for all terrorist group attacks against this country differs from 1.5? Use α=0.05 and Excel/DDXL printout to answer the question ⃝ A. No. The data do not show that the true mean number of suicide bombings differs from 1.5 ⃝ B. Yes. The data show that the true mean number of suicide bombings differs from 1.5 b) A 95% confidence interval for the mean μ, of the population was found to be 1.85±0.510. Answer the question in part a based on the 95% confidence interval ⃝ A. No. The data do not show that the true mean number of suicide bombings differs from 1.5 ⃝ B. Yes. The data show that the true mean number of suicide bombings differs from 1.5 c) Do the inferences derived from the test (part a) and the confidence interval (part b) agree? Explain why or why not. ⃝ A. They agree because both tests use the same value of α ⃝ B. They disagree because a hypothesis test is testing a different event than the confidence interval test ⃝ C. They agree because both tests use the same data set ⃝ D. They disagree because the tests use a different value of α d) What assumption(s) about the data must be true for the inferences to be valid? Select all that apply. ⃝ A. The sample must be greater than 5% of the population ⃝ B. There cannot be any outliners ⃝ C. The population must be approximately normal ⃝ D. The sample must be less than 10% of the population e) Use a graph to check whether the assumption(s) part d is (are) reasonably satisfied. Comment on the validity of the inference. ⃝ A. The assumption(s) seems (seem) reasonably satisfied ⃝ B. The assumption(s) does (do) not seem reasonably satisfied. The data are not random.
• 6. ⃝ C. The assumption(s) does (do) not seem reasonably satisfied. The data are skewed right. ⃝ D. The assumption(s) does (do) not seem reasonably satisfied. The sample is small. ⃝ E. The assumption(s) does (do) not seem reasonably satisfied. The data contain outliers. 12) When planning for a new forest road to be used for tree harvesting, planners must select the location to minimize fractor skidding distance. The skidding distances (in meters) were measured at 20 randomly selected road sites. The data are given below. A logger working on the road claims the mean skidding distance is at least 412 meters. Is there sufficient evidence to refute this claim? Use 450 355 440 280 431 490 400 205 578 544 386 296 185 265 273 399 308 312 137 430 Choose the correct answer below ⃝ A. Do not reject the claim. There is insufficient evidence to indicate that μ<412 meters
• 7. ⃝ B. Reject the claim. There is sufficient evidence to indicate that μ<412 meters ⃝ C. Do not reject the claim. There is sufficient evidence to indicate that μ<412 meters ⃝ D. Reject the claim. There is insufficient evidence to indicate that μ<412 meters 13) For he binomial sample sizes and null-hypothesized values of p in each part, determine whether the sample size is large enough to meet the required conditions for using the normal approximation to conduct a valid large-sample hypothesis test of the null hypothesis Hₒ: p=pₒ Complete parts a through e a) n=499,pₒ=0.05 ⃝ A. The sample size is not large enough to use the normal approximation ⃝ B. The sample size is large enough to use the normal approximation b) n=100,pₒ=0.99 ⃝ A. The sample size is large enough to use the normal approximation ⃝ B. The sample size is not large enough to use the normal approximation c) n=48,pₒ=0.2 ⃝ A. The sample size is large enough to use the normal approximation ⃝ B. The sample size is not large enough to use the normal approximation d) n=20,pₒ=0.2 ⃝ A. The sample size is large enough to use the normal approximation ⃝ B. The sample size is not large enough to use the normal approximation e) n=9,pₒ=0.4 ⃝ A. The sample size is large enough to use the normal approximation ⃝ B. The sample size is not large enough to use the normal
• 8. approximation 14) Suppose a consumer group rated 42 brands of toothpaste based on whether or not the brand carries an American Dental Association (ADA) seal verifying effective decay prevention. The results of a hypothesis test for the proportion of brands with the seal are shown to the right. Complete parts a through c X N Sample p P-value 21 42 0.500000 0.500 a) Give the null and alternative hypothesis for testing whether the true proportion of toothpaste brands with the ADA seal verifying effective decay prevention is less than 0.50. ⃝ A. Hₒ: p=0.50 vs Hₐ: p>0.50 ⃝ B. Hₒ: p=0.50 vs Hₐ: p<0.50 ⃝ C. Hₒ: p<0.50 vs Hₐ: p=0.50 ⃝ D. Hₒ: p=0.50 vs Hₐ: p≠0.50 ⃝ E. Hₒ: p≠0.50 vs Hₐ: p=0.50 ⃝ F. c: p>0.50 vs Hₐ: p=0.50 b) Locate the p-value in the given table. The p-value is _________. (Type an integer or a decimal) c) Make the appropriate conclusion using α=0.10 ⃝ A. Do not reject the null hypothesis since the p-value is not less than the value α ⃝ B. Reject the null hypothesis since the p-value is not less than the value α ⃝ C. Reject the null hypothesis since the p-value is less than the value α ⃝ D. Do not reject the null hypothesis since the p-value is less
• 9. than the value α 15) In order to compare the means of two populations, independent random samples of 385 observations are selected from each population, with the results found in the table to the right. Compare parts a through e Sample 1 Sample 2 x₁ = 5,270 x₂ = 5,231 s₁ = 157 s₂ = 192 a) Use a 95% confidence interval to estimate the difference between the population means (μ₁ -μ₂). Interpret the confidence interval. The confidence interval is (___,___) Interpret the confidence interval. Select the correct answer from the options below. ⃝ A. We are 95% confident that the difference between the population means falls outside of the confidence interval ⃝ B. We are 95% confident that the difference between the population means falls in the confidence interval ⃝ C. We are 95% confident that each of the population means is contained in the confidence interval ⃝ D. We are 95% confident that each of the population means falls outside of the confidence interval b) Test the null hypothesis Hₒ:(μ₁ -μ₂) =0 versus the alternative hypothesis Hₐ: (μ₁ -μ₂)≠0. Give the significance level of the test, and interpret the result. ⃝ A. The p-value is approximately 0.0010, so we do not reject Hₒ for α>0.0010 ⃝ B. The p-value is approximately 0.0020, so we do not reject Hₒ for α>0.0020 ⃝ C. The p-value is approximately 0.0020, so we do not reject Hₒ for α>0.0010
• 10. ⃝ D. The p-value is approximately 0.0010, so we reject Hₒ for α>0.0010 ⃝ E. The p-value is approximately 0.0020, so we reject Hₒ for α>0.0020 ⃝ F. The p-value is approximately 0.0020, so we reject Hₒ for α>0.0010 c) Suppose the test in part b was conducted with the alternative hypothesisHₐ:(μ₁ -μ₂)>0. How would your answer to part b change? ⃝ A. The p-value would be 0.0020, so we would not reject Hₒ for α>0.0020 ⃝ B. The p-value would be 0.0010, so we wouldreject Hₒ for α>0.0020 ⃝ C. The p-value would be 0.0010, so we wouldreject Hₒ for α>0.0010 ⃝ D. The p-value would be 0.0010, so we would not reject Hₒ for α>0.0010 ⃝ E. The p-value would be 0.0020, so we would not reject Hₒ for α>0.0010 ⃝ F. The p-value would be 0.0020, so we wouldreject Hₒ for α>0.0020 d) Test the null hypothesis Hₒ:(μ₁ -μ₂) =27 versus the alternative hypothesis Hₐ: (μ₁ -μ₂)≠27. Give the significance level of the test, and interpret the result. ⃝ A. The p-value is approximately 0.3424, so we do not reject Hₒ for α≤0.3424 ⃝ B. The p-value is approximately 0.1712, so we reject Hₒ for α≤0.3424 ⃝ C. The p-value is approximately 0.1712, so we do not reject Hₒ for α≤0.1712 ⃝ D. The p-value is approximately 0.1712, so reject Hₒ for α≤1712 ⃝ E. The p-value is approximately 0.3424, so reject Hₒ for α≤0.3424
• 11. ⃝ F. The p-value is approximately 0.3424, so we reject Hₒ for α≤0.1712 e) What assumptions are necessary to ensure the validity of the inferential procedures applied in parts a-d? ⃝ A. We must assume that we have two dependent random samples ⃝ B. We must assume that we have two independent random samples ⃝ C. We must assume that the t-distribution should be used ⃝ D. We must assume that we have two small samples 16) To use the t-statistic to test for a diference between the means of two populations, what assumptions must be made about the two populations? About the two samples? What assumption(s) must be made about the two populations? Select all that apply. ⃝ A. Both populations must be selected independently of each other ⃝ B. Both sampled populations must be approximately normally distributed ⃝ C. There must be more than 30 samples selected from each population ⃝ D. Both sampled populations must have approximately equal population variances What assumptions(s) must be made about the two samples? Select all that apply ⃝ A. There must be more than 30 samples selected from each population ⃝ B. The samples must be independent of each other ⃝ C. The samples must be normally distributed 17) Independent random samples from normal populations produced the results shown in the table to the right. Complete parts a through d Sample 1 Sample 2 1.4
• 12. 2.8 3.3 3.3 2.9 3.5 2.9 3.8 3.3 a) Calculate the pooled estimate ơ² s²p=____ (Round to four decimal places as needed) b) Do the data provide sufficient evidence to indicate that μ₂>μ₁? Test using α=0.10 ⃝ No ⃝ Yes c) Find a 90% confidence interval for (μ₁-μ₂). The confidence interval is (___,___) (Round to two decimal places as needed) d) Which of the two inferential procedures, the test of hypothesis in part b of the confidence interval in part c. provides more information about (μ₁-μ₂)? ⃝The test of hypothesis in part b provides more information about (μ₁-μ₂) ⃝Theconfidence interval in part c provides more information about (μ₁-μ₂) 18) Independent random samples are selected from two populations and are used to test the hypothesis Hₒ: (μ₁-μ₂)=0 against the alternative Hₐ:(μ₁-μ₂)≠0. An analysis of 233 observations from population 1 and 313 from population 2 yielded a p-value of 0.111. Complete parts a andb below. a) Interpret the results of the computer analysis. Use α≤0.10. ⃝ A. Since the given α value exceeds this p-value, there is sufficient evidence to indicate that the population means are different
• 13. ⃝ B. Since the p-value exceeds the given value of α, there is insufficient evidence to indicate that the population means are different ⃝ C. Since the given α ex value exceeds this p-value, there is insufficient evidence to indicate that the population means are different. ⃝ D. Since this p-value exceeds the given value of α, there is sufficient evidence to indicate that the population means are different b) If the alternative hypothesis has been Hₐ:(μ₁-μ₂)<0, how would the p-value change? Interpret the p-value for this one- tailed test. p-value = _______ (Type an integer or a decimal) Interpret the p-value for this one-tailed test. Choose the correct interpretation below. ⃝ A. Since the p-value for this one-tailed test exceeds the given value of α, there is insufficient evidence to conclude that the mean for population 1 is significantly lower than the mean for population 2 ⃝ B. Since the given value of α exceeds the p-value for this one-tailed test, there is sufficient evidence to conclude that the mean for population 1 is significantly lower than the mean for population 2 ⃝ C. There is not enough information to answer this question 19) 20) 21) 22) 23)
• 19. Week 4 Income Group Sample Size Mean Road Rage Score Under \$30,000 379 4.6 \$30,000 to \$60,000 392 5.08 Over \$60,000 267 5.15 ANOVA results F-value = 9.02 p-value <0.01 1) Researchers conduct a survey of a representative sample of over 1,000 drivers. Based on how often each driver engaged in road rage behavior, a road rage score was given. The drivers were also grouped by annual income. The data were subjected to an analysis of variance, with the results summarized in the table. Items in RED and underlinedare the multiple choices Reject or Not Reject The null hypothesis that there is no difference in mean road rage scores among variance income classes because there is sufficient or insufficient evidence to indicate a difference in mean road rage scores among various income classes for a α≥0.01.
• 20. The information indicates that the road rage shows no correlation,stays the same,increasesor decreasesas income increases 2) Group 1 1 1 1 1 1 2 2 2 2 2 2 2 2 3 3 3 3 4 4 4 4 4 4 4 Ethics response 2 2 1 4