Question

Exercise 12-13. For this exercise you will use a difference of means test to test the hypothesis that older citizens hold the Supreme Court in higher regard than do younger citizens. The data include two random samples drawn independently. Sample I includes thirty citizens who are forty years of age or older and has a sample mean of 87 and a sample standard deviation of 4. Sample 2 includes twenty- five citizens under age forty and has a sample mean of 85 and a sample standard deviation of 3. Choose a confidence level with which you are comfortable and explain why you chose that level. Then decide if you accept the hypothesis. (Hint: Use the formula for calculating a t-test with independent samples.) Show your work.

Answer 1

Null hypothesis: Ho: 4 = 42 That is, older citizens hold the Supreme Court in same as younger citizens. Alternative hypothesis: Н.: u > , That is, older citizens hold the Supreme Court in higher regard than do younger citizens. Rejection rule: If t>1.6747, then reject the null hypothesis H.

t=X1 - X, 87 - 85 = 2.116 V + The value of the test statistic is t = 2.116. Conclusion: Use a significance level, a = 0.05. Here the value of the test statistic 2.116, which is greater than the critical value 1.6747. That is, t(= 2.116) > 1.6747. Therefore, by the rejection rule, reject the null hypothesis H. Interpretation There is sufficient evidence at level of significance a = 0.05. That is, older citizens hold the Supreme Court in higher regard than do younger citizens.