Reference no: EM132386791

1. David was curious if regular excise really helps weight loss, hence he decided to perform a hypothesis test. A random sample of 5 UMD 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 David 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? Please identify and explain why it is appropriate. 

(b) Let μ1 = mean weight before the exercise regime. Let μ2 = mean weight after the exercise regime. Which of the following statements correctly defines the null hypothesis?

(i) μ1 - μ2 > 0 (μd > 0)

(ii) μ1 - μ2 = 0 (μd = 0)

(iii) μ1 - μ2 < 0 (μd < 0) 

(c) Let μ1 = mean weight before the exercise regime. Let μ2 = mean weight after the exercise regime. Which of the following statements correctly defines the alternative hypothesis?

(a) μ1 - μ2 > 0 (μd > 0)

(b) μ1 - μ2 = 0 (μd = 0)

(c) μ1 - μ2 < 0 (μd < 0) 

(d) Determine the test statistic. Round your answer to three decimal places. Show all work; writing the correct test statistic

(e) Determine the p-value. Round your answer to three decimal places. Show all work; writing the correct critical value, without supporting work, will receive no credit. 

(f) Compare p-value and significance level α. 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? Justify your conclusion.