18W (1)

Page 3 of 28 b) [5 Points] (Ignore Part a) A patient is to take a medical test for high blood pressure. Suppose any reading higher than 130 is considered high blood pressure. b1) What would be the null and the alternative in this case? (2.5 Points) 𝐻𝐻 0 : 𝜇𝜇 = 0 ( 𝜇𝜇 ≤ 0) 𝐻𝐻 1 : 𝜇𝜇 > 0 b2) Explain in words what are Type-I and Type-II errors are in this case? (Note: A generic definition is not enough) (2.5 Points) Type-I error: Conclude that the patient does have High blood pressure when he/she does not. Type-II error: Conclude the patient does not have high blood pressure when he/she does. _ song 9966 22092996275

Page 6 of 28 Part B (Multiple Choice) Form-1 For the following 18 questions, choose the most correct answer and mark it on the SCANTRON form : 1. Identify your form number (Note: if you don’t answer this question correctly you will lose 5 points) A. 1 B. 2 C. 3 D. 4 2. Suppose our p-value is .037. What of the following statements is True? (D) A. We will reject Ho at alpha=.10, but not at alpha=.05 B. We will reject Ho at alpha=.10, .05, or .01 C. We will not reject Ho at alpha=.10, .05, or .01 D. We will reject Ho at alpha=.10 or .05, but not at alpha=.01 E. We will can never reject the null because the p-value is small. 3. The power curve provides the probability of (A) A. rejecting the null hypothesis when the alternative is correct B. accepting the null hypothesis when the alternative is correct C. accepting the null hypothesis when the alternative is correct D. rejecting the alternative when the null is correct E. correctly rejecting the alternative hypothesis 4. In hypothesis testing, we need to assume: (E) I. The sample size is equal or more than 30 II. Distribution of the population is symmetric III. The population variance is known A. I only B. II only C. III only D. I and II only E. None of the above 5. As a researcher you have already calculated the following three confidence intervals using the same data: 90%: (-.29, 6.29), _ song 9966 22092996275

Page 9 of 28 A. the probability of a Type II error increases B. the probability of a Type I error decreases C. the probability we will retain a false Ho decreases D. the error probabilities stay the same E. All of the above 14. When the results are statistically insignificant, this means that _______ (D) A. the obtained probability is equal to or less than α B. the p-value is relatively small C. we can reject Ho D. we cannot accept the alternative E. A and C Questions 15 – 16: The marketing manager for an auto manufacturer is interested in determining the proportion of new compact-car owners who would have purchased a passenger-side inflatable air bag if it had been available for an additional cost of $300. The manager believes from previous information that the proportion is .35. Suppose that a survey of 200 new compact-car owners is selected and 79 indicate that they would have purchased the air bags. Suppose α = 0.05. 15. What would a reasonable hypothesis test be: (C) A. Ho: p=0.35 versus H 1 : p = 0.35 B. Ho: p=0.35 versus H 1 : p > 0.35 C. Ho: p=0.35 versus H 1 : p ≠ 0. 35 D. Ho: p=0.35 versus H 1 : p > 0.35 E. Ho: p=0.35 versus H 1 : p < 0.35 16. The p-value of this test is closest to? (D) A. 5% B. 9.12% C. 14.6%. D. 18.2% E. 21.7% Z stat = 1.334 17. Which of the following are the assumptions that must be satisfied in order to be able to conduct a significance test for the population proportion? (B) I. The data is obtained from a random sample II. The variable is categorical (Non-quantitative) III. The variable is quantitative _ song 9966 22092996275

Page 12 of 28 B. will always be accepted at the 5% level C. will never be tested at the 5% level D. will always be tested at the 5% level E. may be rejected or not rejected at the 5% level 5. Which of the following are the assumptions that must be satisfied in order to be able to conduct a significance test for the population proportion? (B) I. The data is obtained from a random sample II. The variable is categorical (Non-quantitative) III. The variable is quantitative IV. The population size is more than 30 V. The population is normally distributed VI. The sample size is sufficiently large VII. The sampling distribution of pˆ is approximately normal A. I, IV, and VII B. I, II, and VII C. I, III, and VI D. I, IV, and V E. V, IV, and III 6. For testing the hypotheses H 0 : P = 0.8 versus H 1 : P ≠ 0.8 at 1% significance level, we obtain a sample of n = 100 and p = 0.75. The Type-I error for this test is closest to: (C) A. 0.100 B. 0.140 C. 0.212 D. 0.010 E. 0.020 Questions 7 – 8: The marketing manager for an auto manufacturer is interested in determining the proportion of new compact-car owners who would have purchased a passenger-side inflatable air bag if it had been available for an additional cost of $300. The manager believes from previous information that the proportion is .35. Suppose that a survey of 200 new compact-car owners is selected and 79 indicate that they would have purchased the air bags. Suppose α = 0.05. 7. What would a reasonable hypothesis test be: (C) A. Ho: p=0.35 versus H 1 : p = 0.35 B. Ho: p=0.35 versus H 1 : p > 0.35 C. Ho: p=0.35 versus H 1 : p ≠ 0.35 D. Ho: p=0.35 versus H 1 : p > 0.35 E. Ho: p=0.35 versus H 1 : p < 0.35 _ song 9966 22092996275

Page 15 of 28 A. the probability of a Type II error increases B. the probability of a Type I error decreases C. the probability we will retain a false Ho decreases D. the error probabilities stay the same E. All of the above 16. When the results are statistically insignificant, this means that _______ (D) A. the obtained probability is equal to or less than α B. the p-value is relatively small C. we can reject Ho D. we cannot accept the alternative E. A and C 17. Suppose our p-value is .037. What of the following statements is True? (D) A. We will reject Ho at alpha=.10, but not at alpha=.05 B. We will reject Ho at alpha=.10, .05, or .01 C. We will not reject Ho at alpha=.10, .05, or .01 D. We will reject Ho at alpha=.10 or .05, but not at alpha=.01 E. We will can never reject the null because the p-value is small. 18. The power curve provides the probability of (A) A. rejecting the null hypothesis when the alternative is correct B. accepting the null hypothesis when the alternative is correct C. accepting the null hypothesis when the alternative is correct D. rejecting the alternative when the null is correct E. correctly rejecting the alternative hypothesis _ song 9966 22092996275

Page 18 of 28 C. 0.01 < p-value < 0.05 D. 0.05 < p-value < 0.10 E. Can’t be determined. Questions 10 – 11: The marketing manager for an auto manufacturer is interested in determining the proportion of new compact-car owners who would have purchased a passenger-side inflatable air bag if it had been available for an additional cost of $300. The manager believes from previous information that the proportion is .35. Suppose that a survey of 200 new compact-car owners is selected and 79 indicate that they would have purchased the air bags. Suppose α = 0.05. 10. What would a reasonable hypothesis test be: (C) A. Ho: p=0.35 versus H 1 : p = 0.35 B. Ho: p=0.35 versus H 1 : p > 0.35 C. Ho: p=0.35 versus H 1 : p ≠ 0.35 D. Ho: p=0.35 versus H 1 : p > 0.35 E. Ho: p=0.35 versus H 1 : p < 0.35 11. The p-value of this test is closest to? (D) A. 5% B. 9.12% C. 14.6%. D. 18.2% E. 21.7% Z stat = 1.334 12. Which of the following are the assumptions that must be satisfied in order to be able to conduct a significance test for the population proportion? (B) I. The data is obtained from a random sample II. The variable is categorical (Non-quantitative) III. The variable is quantitative IV. The population size is more than 30 V. The population is normally distributed VI. The sample size is sufficiently large VII. The sampling distribution of pˆ is approximately normal A. I, IV, and VII B. I, II, and VII C. I, III, and VI D. I, IV, and V E. V, IV, and III _ song 9966 22092996275

Page 21 of 28 Part B (Multiple Choice) Form-4 For the following 18 questions, choose the most correct answer and mark it on the SCANTRON form : 1. Identify your form number (Note: if you don’t answer this question correctly you will lose 5 points) A. 1 B. 2 C. 3 D. 4 2. In hypothesis testing, we need to assume: (E) I. The sample size is equal or more than 30 II. Distribution of the population is symmetric III. The population variance is known A. I only B. II only C. III only D. I and II only E. None of the above 3. As a researcher you have already calculated the following three confidence intervals using the same data: 90%: (-.29, 6.29), 95%: (-.92, 6.92), 99%: (-2.13, 8.13), Now she wants to test H 0 : μ = -2.5 vs. H 1 : μ ≠ -2.5. Regarding the p-value, which of the following statements is true? (A) A. P-value < 0.01 B. P-value > 0.10 C. 0.01 < p-value < 0.05 D. 0.05 < p-value < 0.10 E. Can’t be determined. 4. If a hypothesis is rejected at the 6% level of significance, it (E) A. will always be rejected at the 5% level _ song 9966 22092996275

Page 22 of 28 B. will always be accepted at the 5% level C. will never be tested at the 5% level D. will always be tested at the 5% level E. may be rejected or not rejected at the 5% level 5. Which of the following are the assumptions that must be satisfied in order to be able to conduct a significance test for the population proportion? (B) I. The data is obtained from a random sample II. The variable is categorical (Non-quantitative) III. The variable is quantitative IV. The population size is more than 30 V. The population is normally distributed VI. The sample size is sufficiently large VII. The sampling distribution of pˆ is approximately normal A. I, IV, and VII B. I, II, and VII C. I, III, and VI D. I, IV, and V E. V, IV, and III 6. For testing the hypotheses H 0 : P = 0.8 versus H 1 : P ≠ 0.8 at 1% significance level, we obtain a sample of n = 100 and p = 0.75. The Type-I error for this test is closest to: (C) A. 0.100 B. 0.140 C. 0.212 D. 0.010 E. 0.020 Questions 7 – 8: The marketing manager for an auto manufacturer is interested in determining the proportion of new compact-car owners who would have purchased a passenger-side inflatable air bag if it had been available for an additional cost of $300. The manager believes from previous information that the proportion is .35. Suppose that a survey of 200 new compact-car owners is selected and 79 indicate that they would have purchased the air bags. Suppose α = 0.05. 7. What would a reasonable hypothesis test be: (C) A. Ho: p=0.35 versus H 1 : p = 0.35 B. Ho: p=0.35 versus H 1 : p > 0.35 C. Ho: p=0.35 versus H 1 : p ≠ 0.35 D. Ho: p=0.35 versus H 1 : p > 0.35 E. Ho: p=0.35 versus H 1 : p < 0.35 _ song 9966 22092996275

Page 23 of 28 8. The p-value of this test is closest to? (D) A. 5% B. 9.12% C. 14.6%. D. 18.2% E. 21.7% Z stat = 1.334 Questions 9 – 10 : The 95% confidence interval for a population proportion is [0.10, 0.14]: 9. The point estimate for the population proportion is: (B) A. 0.10 B. 0.12 C. 0.14 D. 0.32 E. None of the above 10. The sample size must be closest to: (C) A. 1418 B. 1231 C. 1014 D. 971 E. None of the above 0.02 = 1.96*sqrt(0.12*0.88/n) Questions 11 – 13 : A normal population has mean µ and standard deviation 10. The hypotheses to be tested are H 0 : µ = 10 versus H 1 : µ > 10. 11. Which would result in the highest power? (D) A. µ 1 = 11; n =10 B. µ 1 = 12; n =10 C. µ 1 = 11; n =100 D. µ 1 = 12; n =100 E. µ 1 = 12.2; n =10 12. If a random sample has 36 observations, the true population mean is 14, and the significance level is 1% then the probability of a Type II error is approximately: (B, A is allowed) _ song 9966 22092996275

Page 24 of 28 A. 0.528 B. 0.462 C. 0.415 D. 0.331 E. 0.054 0279 . 0 5 . 0 ) 07 . 0 6 10 14 88 . 13 ( ) 14 | 88 . 13 ( 88 . 13 36 10 33 . 2 10 − = − = − < = = < = × + = Z P x P x µ   13. If you wish the power of the test in the previous question to be at least 95% the sample size should be at least: (E) A. 178 B. 154 C. 145 D. 112 E. 99 14. The director of admissions at a large university advises parents of incoming students about the cost of textbooks during a typical semester. A sample of 36 students enrolled in the university indicates a sample average cost of $315.40 with a sample standard deviation of $43.20. Is there enough evidence that the population average is above $300? What would be the p-value for this test: (D) A. > .1 B. > .2 C. between 0.025 and .05 D. between .01 and .025 E. <0.01 𝑡𝑡 50 = 315.4 − 300 43.20/ √ 36 = 2.139 15. In a hypothesis testing if α is changed from .01 to .05, _____ (C) ( ) 75 . 98 ) 14 10 ( 10 ) 645 . 1 33 . 2 ( ) ( 2 2 2 2 0 2 2 ≅ − + = − + = a B z z n µ µ σ α _ song 9966 22092996275

Page 25 of 28 A. the probability of a Type II error increases B. the probability of a Type I error decreases C. the probability we will retain a false Ho decreases D. the error probabilities stay the same E. All of the above 16. When the results are statistically insignificant, this means that _______ (D) A. the obtained probability is equal to or less than α B. the p-value is relatively small C. we can reject Ho D. we cannot accept the alternative E. A and C 17. Suppose our p-value is .037. What of the following statements is True? (D) A. We will reject Ho at alpha=.10, but not at alpha=.05 B. We will reject Ho at alpha=.10, .05, or .01 C. We will not reject Ho at alpha=.10, .05, or .01 D. We will reject Ho at alpha=.10 or .05, but not at alpha=.01 E. We will can never reject the null because the p-value is small. 18. The power curve provides the probability of (A) A. rejecting the null hypothesis when the alternative is correct B. accepting the null hypothesis when the alternative is correct C. accepting the null hypothesis when the alternative is correct D. rejecting the alternative when the null is correct E. correctly rejecting the alternative hypothesis _ song 9966 22092996275

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Page 27 of 28 _ song 9966 22092996275

Page 28 of 28 Formula sheet Inference about µ when σ 2 known: Test statistic: n X z σ µ − = CI estimator: n z X σ α 2 / ± Sample size to estimate µ ± τ : 2 2 /       = τ σ α z n Inference about µ when σ 2 unknown: Test statistic: n s X t µ − = CI estimator: n s t X 2 / α ± 1 − = n ν Inference about p (population proportion): Test statistic: n p p p p z / ) 1 ( ˆ − − = CI estimator: n p p z p / ) ˆ 1 ( ˆ ˆ 2 / − ± α Sample size to estimate p ± τ : 2 2 / ) ˆ 1 ( ˆ         − = τ α p p z n Sample Size for Beta error: ( ) 2 0 2 2 ) ( a B z z n µ µ σ α − + = _ song 9966 22092996275