Question

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A health educator was interested in determining whether college students at her college really do gain weigh during their freshman year. A random sample of 5 college students was chosen and the weight for each student was recorded in August and May. 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 2 3 4 5	175                        180 170                        164 135                        142 160                        166 200                        208

(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.

Answer 1

(a)

Here we have paired data so paired t test will be used.

Assumption: The difference in weights (August - May) are normally distributed.

(b)

Let d= August - May

The null hypothesis is

(c)

(d)

Following table shows the calculations:

August	May	d=August-May	(d-mean)^2
175	180	-5	1
170	164	6	100
135	142	-7	9
160	166	-6	4
200	208	-8	16
Total		-20	130

Sample size n=5

So

So test statistics will be

(e)

Degree of freedom: df=4

The p-value is: 0.0958

Excel function used for p-value: "=TDIST(1.57,4,1)"

(f)

Since p-value is greater than 0.05 so we fail to reject the null hypothesis.

(g)

There is no evidence to conclude that college students gain weight during their freshman year.