Exercise Problems on Chapter 11. One-Sample Hypothesis Testing This set of exercise problems has 50 Questions, worth a total of 50 points. 1. Inductive reasoning allows one to draw a conclusion about _____ from ______. a. c. e. 2. The null hypothesis contains by convention ______. a. c. e. 3. an inequality sign a multiplication and/or division sign no equality sign a plus and/or minus sign a value of zero or larger b. d. no inequality sign a multiplication and/or division sign original; H0 or Ho important; H0 or Ho new; not H0 b. d. original; H1 or Ha important; H1 or Ha The purpose of a hypothesis testing is to disapprove the _____ hypothesis in order to prove the _____ hypothesis. a. c. e. 6. b. d. The null hypothesis is also called the ____ hypothesis and expressed as _____. a. c. e. 5. an equality sign a plus and/or minus sign a value of zero or larger An alternative hypothesis contains by convention _____. a. c. e. 4. a sample; a population b. a sample; another sample a population; a sample d. a population; another population the degree of dispersion; a standard normal distribution alternative; null opposite; alternative new; old b. d. null; alternative null; another null An example of a null hypothesis in single hypothesis testing is _____ and that of composite or joint hypothesis testing is _____. a. H0: 1 = 2 = 0; H0: = 0 b. c. d. e. 7. directional or upper-tail only (a) and (b) of the above two; one one; one more than 2; only one b. d. two; two one; two a measure of Type I error. equal to 1 minus a confidence level. only (b) and (c) of the above. b. d. a measure of Type II error. only (a) and (c) of the above. Rejecting the null hypothesis when it is in fact true involves an error called _____. a. b. c. d. e. 12. one-tailed or directional b. directional or lower-tail d. only (a) and (c) of the above A significance level, , is a. c. e. 11. two-tailed only (a) and (c) of the above A two-tail test means that there is/are ______ rejection region(s) and a one-tail test means that there is/are _____ rejection region(s). a. c. e. 10. one-tailed b. composite d. only (b) and (c) of the above When an alternative hypothesis is states as Ha: > 0, it means a _____ test. a. c. e. 9. H0: 0 H0: 1 = 2 = 0 H0: 1 = 2 = 0 H0: 1 2 0 When an alternative hypothesis is stated as Ha: 0, it means a _____ test. a. c. e. 8. H0: 1 = 2 = 0; H0: 0; H0: = 0; H0: 0; Type I error measured by a significance level. Type II error measured by a significance level. Type I error measured by a power of the test. Type II error measured by a power of the test. Type I error measured by a confidence level. Accepting the null hypothesis when it is in fact false involves an error called _____. a. b. c. d. e. 13. The power of the test is measured as _____. a. d. 14 (1- ) ( + ) c. to use experts of error minimization to decrease the sample size to increase the sample size to choose a significance level of zero to choose a power of the test to be zero the critical Z-value approach the confidence interval approach none of the above b. d. the p-value approach all of the above If one sees a set of hypotheses as: H0: < k vs. H1: > k, it is called a/an _____ test and if one sees a set of hypotheses as: H0: > k vs. H1: < k, it is called a/an _____ test. a. c. e. 17. b. c. Which of the following is an approach (or a method) that can be used to conduct hypothesis testing? a. c. e. 16. (1- ) The best way to minimize both Type I and Type II errors is _____. a. b. c. d. e. 15. Type II error often represented as (1- ). Type I error often represented as . Type II error often represented as . Type I error often represented as . Type II error often represented as . one-tail; upper-tail regular two-tail; reverse two-tail lower-tail; one-tail b. d. lower-tail; upper-tail upper-tail; lower-tail The decision criterion for a two-tail test, using the critical Z-value approach and a significance level of , includes _____. a. If Zc Z / 2 , or Z / 2 Zc +Z / 2 , then fail to reject H0: =k accept H0 b. If Zc Z , or Z Zc +Z , then fail to reject H0: =k accept H0 18. 19. c. If Zc Z / 2 , or Z / 2 Zc +Z / 2 , then reject H0: =k accept Ha d. If Zc Z , or Z Zc +Z , then reject H0: =k accept Ha e. none of the above. The decision criterion for an upper-tail test, using the critical Z-value approach and a significance level of , includes _____. a. If Zc Z / 2 , or Z / 2 Zc +Z / 2 , then fail to reject H0 accept H0 b. c. d. e. If Zc < Z, then fail to reject H0 accept H0 If Zc > Z, then fail to reject H0 accept H0 If Zc > Z, then reject H0 accept Ha only (b) and (d) of the above The decision criterion for a lower-tail test, using the critical Z-value approach and a significance level of , includes _____. a. b. c. d. e. 20. The decision criterion for a two-tail test, using the p-value or the prob-value approach and a significance level of , includes _____. a. b. c. d. e. 21. If Zc < -Z/2, then fail to reject H0 accept H0 If Zc > -Z, then fail to reject H0 accept H0 If Zc < -Z, then reject H0 accept Ha only (b) and (c) of the above none of the above If p-value > , then fail to reject the null hypothesis accept H0 If p-value < , then fail to reject the null hypothesis accept H0 If p-value > /2, then fail to reject the null hypothesis accept H0 If p-value < /2, then fail to reject the null hypothesis accept H0 none of the above The decision criterion for a two-tail test, using the p-value or the prob-value approach and a significance level of , includes _____. a. b. c. d. e. If p-value > , then reject the null hypothesis accept Ha If p-value < , then reject the null hypothesis accept Ha If p-value > /2, then reject the null hypothesis accept Ha If p-value < /2, then reject the null hypothesis accept Ha none of the above 22. The decision criterion for an upper-tail test, using the p-value or the prob-value approach and a significance level of , includes _____. a. b. c. d. e. 23. The decision criterion for a lower-tail test, using the p-value or the prob-value approach and a significance level of , includes _____. a. b. c. d. e. 24. b. c. d. e. if a hypothesized value such as = k falls within a confidence interval, fail to reject the null hypothesis accept H0 if a hypothesized value such as = k falls outside a confidence interval, fail to reject the null hypothesis accept H0 if a hypothesized value such as = k falls within a confidence interval, reject the null hypothesis accept Ha only (b) and (c) of the above. none of the above For hypothesis testing, a Z-test is used when the _____ standard deviation is _____ whereas a t-test is used when it is _____. a. c. e. 26. If p-value > , then reject the null hypothesis accept Ha If p-value < , then reject the null hypothesis accept Ha If p-value > /2, then reject the null hypothesis accept Ha If p-value < /2, then reject the null hypothesis accept Ha none of the above The decision criterion for a two-tail test, using the confidence interval approach and a significance level of , includes _____. a. 25. If p-value > , then fail to reject the null hypothesis accept H0 If p-value < , then fail to reject the null hypothesis accept H0 If p-value > /2, then fail to reject the null hypothesis accept H0 If p-value < /2, then fail to reject the null hypothesis accept H0 none of the above population; known; unknown sample; known; unknown population; unknown; unknown b. d. population; unknown; known sample; unknown; known The decision criteria based on a critical (Z- or t-) value approach for accepting or rejecting a null hypothesis are ______. a. b. c. d. e. more complicated for a Z-test because it relies on the sample standard deviation which is difficult to calculate. more complicated for a t-test than a Z-test due to the degrees-of-freedom issue. more complicated for a Z-test than a t-test due to the degrees-of-freedom issue. more complicated for a t-test because it relies on the standardized normal probability distribution. only (a) and (c) of the above Use the following general situation to answer Questions 27 through 37. Suppose that you are hired as a consultant to examine the production process of sugarglazed donuts. The donut machine used is designed to put on 10 grams of sugar with an allowable variability, as measured by the standard deviation, of 1.5 grams for each donut made. In order to see if the donut machine is doing working properly, you took a random sample of 25 donuts and found that the average amount of sugar on each donut was 11 grams. 27. If you wish to examine if the observed average of 11 grams per donut is statistically the same as the machine-designed weight of 10 grams, which of the following accurately states the null hypothesis that you wish to test? a. d. 28. b. e. H0: = 11 c. none of the above H1: = 10 Which test statistic would you use? a. d. 29. H1: = 11 H0: = 10 Z-value Chi-square value b. e. t-value c. none of the above F-value Assuming that you are to test the following hypothesis using the above information and a critical Z-value approach at a 5% significance level, H0: = 10.5 vs. H1: 10.5 you would find the calculated Z-value, Zc, to be _____ and the critical (or table) Z-value to be _____. a. d. 30. 1.67; 1.96 accept the null hypothesis. fail to reject the null hypothesis none of the above b. d. reject the null hypothesis. only (a) and (c) of the above accept the null hypothesis. fail to reject the null hypothesis none of the above b. d. reject the null hypothesis. only (a) and (c) of the above accept the null hypothesis. fail to reject the null hypothesis none of the above b. d. reject the null hypothesis. only (a) and (c) of the above Using the p-value approach, if the calculated Z-value is 2.27 for a two-tail test, you conclusion would be to _______ at a 1% significance level. a. c. e. 34. c. Using the p-value approach, if the calculated Z-value is 2.27 for a two-tail test, you conclusion would be to _______ at a 5% significance level. a. c. e. 33. 0.33; 1.645 1.96; 1.96 If the absolute value of the calculated Z-value is less than the critical (or table) Zvalue, your conclusion would be _____. a. c. e. 32. b. e. If the absolute value of the calculated Z-value is greater than the critical (or table) Z-value, your conclusion would be _____. a. c. e. 31. 0.33; 1.96 1.67; 1.645 accept the null hypothesis. fail to reject the null hypothesis none of the above b. d. reject the null hypothesis. only (a) and (c) of the above Using the confidence-interval approach, if the sample mean is 11 grams and a population standard deviation of 1.5 grams, the 95% confidence interval for a two-tail test is found to be _____. a. c. between 9.5 and 12.5 between 10.41 and 11.59 b. d. between 8 and 14 between 8.06 and 13.94 e. 35. Using the confidence-interval approach for a two-tail test, if the hypothesized value falls within the constructed confidence interval, your conclusion would be to _____. a. c. e. 36. between 9.41 and 10.59 accept the null hypothesis fail to reject the null hypothesis none of the above b. d. reject the null hypothesis only (a) and (c) of the above Assuming that you are to test the following hypothesis using the above information and a critical Z-value approach at a 5% significance level, H0: > 10.5 vs. H1: < 10.5 you would find the calculated Z-value, Zc, to be _____ and the critical (or table) Z-value to be _____. a. d. 37. 0.33; -1.96 1.67; -1.645 b. e. 0.33; -1.645 1.96; -1.645 c. 1.67; -1.96 If the calculated Z-value is greater than the critical (or table) Z-value for the above one-tail test, your conclusion would be _____. a. b. c. d. e. accept the null hypothesis that > 10.5. reject the null hypothesis that > 10.5. fail to reject the null hypothesis that > 10.5. only (a) and (c) of the above none of the above Use the following general situation to answer Questions 38 through 46. Suppose that you are hired as a marketing consultant to examine the average age of shoppers in a major shopping mall. After asking randomly chosen 100 people of their age, you received 49 unbiased truthful answers. Upon tabulation, you found that the average age was 35 with a variance of 1.96. 38. If you wish to examine if the observed average age of 35 is statistically the same as the average age of 38 that the president of the shopping mall strongly believes on the basis of his daily observations, which of the following accurately states the null hypothesis that you wish to test? a. d. 39. b. e. H0: = 38 H0: > 35 c. H0: > 35 Which test statistic would you use? a. d. 40. H0: = 35 H0: < 38 Z-value Chi-square value b. e. t-value c. none of the above F-value Assuming that you are to test the following hypothesis using the above information and a critical t-value approach at a 5% significance level, H0: = 36.5 vs. H1: 36.5 you would find the calculated t-value, tc, to be _____ and the critical (or table) tvalue to be _____ and the corresponding degrees of freedom to be _____. a. c. e. 41. -7.5; +2.0096; 49 5.357; +2.0096; 49 accept the null hypothesis. fail to reject the null hypothesis none of the above b. d. reject the null hypothesis. only (a) and (c) of the above If the absolute value of the calculated t-value is less than the critical (or table) tvalue, your conclusion would be _____. a. c. e. 43. b. d. If the absolute value of the calculated t-value is greater than the critical (or table) t-value, your conclusion would be _____. a. c. e. 42. -7.5; +2.0106; 48 5.357; +2.0106; 48 -7.65; +2.0106; 48 accept the null hypothesis. fail to reject the null hypothesis none of the above b. d. reject the null hypothesis. only (a) and (c) of the above Using the p-value approach, if the calculated t-value is 2.0423 with 30 degrees of freedom for a two-tail test, you conclusion would be to _______ at a 1% significance level. a. c. e. 44. b. d. reject the null hypothesis. only (a) and (c) of the above Using the confidence-interval approach, if the sample mean age is 35 and the sample variance is 1.96 on the basis of 49 observations, the 95% confidence interval for a two-tail test is found to be _____. a. c. e. 45. accept the null hypothesis. fail to reject the null hypothesis none of the above between 33.04 and 36.96 between 34.6 and 35.4 between 31.06 and 38.94 b. d. between 33.6 and 36.4 between 34.72 and 35.28 Assuming that you are to test the following hypothesis using the above information and a critical t-value approach at a 5% significance level, H0: < 36.5 vs. H1: > 36.5 you would find the calculated t-value, tc, to be _____ and the critical (or table) tvalue to be _____. a. d. 46. b. e. 7.5; 2.0096 -7.5; 1.6772 c. 5.357; 2.0106 If the calculated t-value is greater than the critical (or table) t-value for the above one-tail test, your conclusion would be _____. a. b. c. d. e. 47. -7.5; 2.0106 5.357; 1.6772 accept the null hypothesis that < 36.5. reject the null hypothesis that < 36.5. fail to reject the null hypothesis that < 36.5. only (a) and (c) of the above none of the above When conducting a two-tail test, if the p-value is ____ than the chosen significance level, you would reject the _____ hypothesis at the ______. a. c. e. smaller; null; p-value b. smaller; alternative; significance level smaller; null; significance level large; null; significance level d. larger; alternative; p-value 48. When conducting hypothesis testing, 3 approaches are commonly used. The three approaches include _____. a. b. c. d. e. 49. When using the 3 approaches to hypothesis testing, the conclusion drawn _____. a. b. c. d. e. 50. the critical Z- or t-value approach the confidence or significance approach the p-value or the prob-value approach all of the above only (a) and (c) of the above should be the same regardless of which approach is used. can be different depending upon what approach is used. the p-value or prob-value approach yields the most accurate and consistent result. only (a) and (c) of the above only (b) and (c) of the above The confidence interval associated with a 1% significance level is _____ that associated with a 5% significance level. a. narrower than b. wider than c. the same as d. can be narrower and can be wider depending on the size of the hypothesized value e. is a better measure of accuracy than