David was curious if regular excise really helps weight loss, hence he decided to perform a hypothesis test. A random sample of 5 UMUC 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

(couldn't upload a table here so the /'s represent the sections)

• 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.
• 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?

1 - 2 > 0 (d > 0)

1 - 2 = 0 (d = 0)

1 - 2 < 0 (d < 0)

• 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 - 2 > 0 (d > 0)

1 - 2 = 0 (d = 0)

1 - 2 < 0 (d < 0)

• Determine the test statistic. Round your answer to three decimal places. Show all work; writing the correct test statistic, without supporting work, will receive no credit.
• 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.
• Compare p-value and significance level . What decision should be made regarding the null hypothesis (e.g., reject or fail to reject) and why?
• Is there sufficient evidence to support the claim that regular exercise helps weight loss? Justify your conclusion.

Show all work, including any Excel formulas/functions.