Question

Label the following 2-sample tests as: Proportions, Independent, and Dependent (matched-pairs). Determine the null and alternative hypothesis and whether the test is one-tailed or two-tailed. Then explain in detail the reasons behind your answers. You do not have to work the problems out. 1. The pre-test scores for 6 students were: 5, 5, 6, 7, 7, 8. The post-test scores for the same 6 students were: 7, 6, 7, 7, 9, 9. Is there a statistically significant difference between the two scores if we assume that the post-test scores were higher at the .01 level? 2. One group of 8 students took a pre-test, while another group of 7 students took a post-test. The following are the results: Pre-test: 5,6,4,3,4,6,6,7. Post-test: 6,6,8,7,9,8,8. Is there a difference between pre and post-test scores at the .01 level? 3. Two surveys were conducted asking participants whether they thought the morality of Americans was decaying or not. The percent of those who thought there was a decay in morality was 56% in survey 1, while the percent of those who thought there was a decay in morality was 59.5% in survey 2. Test the claim survey 2's percent was larger at the .05 level.

Answer 1

1. Here, the sample values are of the same candidate. Hence, the 2-sample test is Dependent.
   
   
   Here, we are to test if the pre-test value and post-test values are significantly 'different' than the pre-test score. Hence, the Hypothesis is:
   
   where,
   
   Since, the alternative is 'different', that is, two-sided, the test is a two-sided test.
   
   
2. Here, the sample values are of different candidate. Hence, the 2-sample test is Independent.
   
   Here, we are to test if the pre-test value and post-test values are significantly 'different' than the pre-test score. Hence, the Hypothesis is:
   
   
   Since, the alternative is 'different', that is, two-sided, the test is a two-sided test.
   
   
3. Since, the values are proportions, that is, the percent of participants who have think the mortality of Americans was decaying, The 2-sample test is Proportion.
   
   Here, we are to test the claim that survey 2's percent was larger than survey 1's. So, the Hypothesis is set as:
   
   
   Since, the alternative is 'greater than', that is, only one-sided, the test is a one-sided test.
   
   

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