Mimi was curious if regular excise really helps weight loss, hence she decided to perform a hypothesis test. A random sample of 5 students was chosen. The students took a 30- minute exercise every day for 6 months. The weight was recorded for each individual before and after the exercise regimen. Does the data below suggest that the regular exercise helps weight loss? Assume Mimi wants to use a 0.05 significance level to test the claim.

Weight (pounds)

Subject Before After

1 190 180

2 170 160

3 185 190

4 160 160

5 200 190

(a) What is the appropriate hypothesis test to use for this analysis ( z-test for two proportions, t-test for two proportions, t-test for two dependent samples (matched pairs), or t-test for two independent samples) Why?

(b) Let 1 = mean weight before the exercise regime. Let 2 = mean weight after the exercise regime. Which of the following statements correctly defines the null hypothesis? (i) 1 - 2 > 0 (d > 0)

(ii) 1 - 2 = 0 (d = 0)

(iii) 1 - 2 < 0 (d < 0)

(c) Let 1 = mean weight before the exercise regime. Let 2 = mean weight after the exercise regime. Which of the following statements correctly defines the alternative hypothesis?

(1) 1 - 2 > 0 (d > 0)

(2) 1 - 2 = 0 (d = 0)

(3) 1 - 2 < 0 (d < 0)

(d) How would you determine the test statistic.

(e) How would you determine the p-value?

(f) Compare p-value and significance level . What decision should be made regarding the null hypothesis (e.g., reject or fail to reject) and why?

(g) Is there sufficient evidence to support the claim that regular exercise helps weight loss?Why?