Question

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.

	Weight (pounds)
Student	August	May
1	175	180
2	170	164
3	135	142
4	160	166
5	200	208

(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) student's t distribution is the appropriate hypothesis test for the given conditions because the population standard deviation is unknown and the sample size is also less than 30. So, student's t distribution is best suited for this hypothesis testing.

(B) we always assume that there is no difference between the means as null hypothesis, so this statement matching option second

so, correct answer is (ii) option ?1 - ?2 = 0 (?d = 0)

(C) For alternate hypothesis, assume the claim to be true and the claim is that students gain weight in their college freshman year

this means the weight in May must be more than weight in August

so, alternate hypothesis will be ?1 more than ?2 or difference of ?1 and ?2 must be greater than 0

so, option (i) is correct

(D) we will be using pooled t test assuming that the samples have equal variances

formula for t test is

Using the excel function AVERAGE and STDEV.S, we can get the value of mean and sample standard deviation

we get

first, we calculate Sp

Sp =

setting the values, we get

Sp =

Now, setting the value of x1,x2,n1,n2 and Sp in the formula for t statistic

we get

test statistic t = =

this gives

test statistic t = 4/15.15 = 0.264

(E) Using student's t distribution table for t = 0.264, degree of freedom = n1+n2-2 = 10-2 = 8

we get p value = 0.399

(F) Since p value is more than 0.05, we can say that p valie is insignificant. We fail to reject the null hypothesis because p value is insignificant

(G) We can conclude that there is not enough evidence to support the claim that students gain weight during their freshman using the data provided because we failed to reject the null hypothesis as p value calculated is insignificant at desired significance level.