A health educator was interested in determining whether college students at her college really do gain weight during their freshman year. A random sample of 5 college students was chosen and the weight for each student was recorded in August (the beginning of the freshman year) and May (the end of the freshman year). Does the data below suggest that college students gain weight during their freshman year? The health educator wants to use a 0.05 significance level to test the claim.

Weight (pounds)

Student August May

1 180 182

2 170 175

3 135 140

4 162 160

5 200 200

(a) What is the appropriate hypothesis test to use for this analysis? Please identify and explain why it is appropriate.

(b) Let 1 = mean weight in May. Let 2 = mean weight in August. 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 in May. Let 2 = mean weight in August. Which of the following statements correctly defines the alternative hypothesis?

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

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

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

(d) Determine the test statistic. Round your answer to three decimal places. Describe method used for obtaining the test statistic.

(e) Determine the p-value. Round your answer to three decimal places. Describe method used for obtaining 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) What do the results of this study tell us about freshman college student weight gain? Justify your conclusion.