Question

Use the following to answer questions 1-4. The average house hold size in a certain region several years ago was 3.14. A sociologist wishes to test, at 5% level of significance, whether it is different now. Perform the test using the information collected by the sociologist; in a random sample of 75 households, the average size was 2.98 persons, with sample standard deviation 0.82 persons. 1. Set up the null and alternative hypothesis to test the researcher’s claim. a. ?0:?=2.98 ?? ??:?≠2.98 b. ?0:?=2.98 ?? ??:?>2.98 c. ?0:?=2.98 ?? ??:?<2.98 d. ?0:?=3.14 ?? ??:?≠3.14 e. ?0:?≥3.14 ?? ??:?<3.14 2. The value of the standardized test statistic is a. 1.69 b. -1.69 c. 0.20 d. -0.20 e. -1.53 3. The p-value of this test is a. 0.0455 b. 0.4207 c. 0.0910 d. 0.0500 e. cannot be determined 4. The Rejection region and decision of the test: a. Rejection region: (−∞, −1.645] ∪ [1.645, ∞); Decision: Reject the null hypothesis b. Rejection region: (-∞, -1.645]; Decision: Reject the null hypothesis c. Rejection region: (-∞, -1.96]∪[1.96, ∞); Decision: Reject the null hypothesis d. Rejection region: (-∞, -1.96]∪[1.96, ∞); Decision: Fail to reject the null hypothesis e. Rejection region: (-∞, -1.96]; Decision: Fail to reject the null hypothesis

Answer 1