Question

Suppose you are interested in deciding if a particular diet is effective in changing people's weight. You decide to run a "within subject" experiment. You select 6 people and weigh each of them. Two weeks and you weigh them again. For each person you compute how much weight they lose over this period. You find : Non-diet (subject 1-6): 0,8,3,2,-10,-1. You then put them on the diet and weigh them again after two weeks and compute how much they lose over this period. Diet: (subject 1-6): 1,6,4,3,-8,2.

a. compute the null and alternative hypotheses

b. compute the mean and standard deviation of the difference distribution

c. how many degrees of freedom?

d. assume the null hypothesis is true and compare the t-statistic

e. compute p-value

f. at an alpha =0.05 would you accept or reject null?

Suppose the research assistant lost the information that linked the subjects identity across the two weight loss periods. This makes it impossible to run a paired t-test. Rather than start over:

a. compute the mean and standard deviation

b. compute the two sample t-statistic

c. how many degrees of freedom?

d. compute p-value

e. how does this p-value compare to the one you just compared using the paired t-test?

Answer 1

a)

Claim: A particular diet is effective in changing people’s weight.

b)

Sample size = n = 6

Sample mean of difference = = - 1

Sample standard deviation of difference = = 1.673

c)

Degrees of freedom = n - 1 = 6 - 1 = 5

d)

Test statistic is

e)

P-value = P(T < - 1.46) = 0.1016

f) P-value > 0.05 we fail to reject null hypothesis.

Accept