Question

Paired Samples t-test (30pts) 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 weight each of them. Two weeks, you weight them again. For each person you compute how much weight they lost over this period. This is what 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 lost over this period. Diet(subject 1-6) : 1 6 4 3 -8 2

a) State the null and alternative hypotheses (2pts)

b) Compute the mean and standard deviation of the difference distribution (4pts)

c) How many degrees of freedom do you have? (3pts)

d) Assume the Null Hypothesis is True and compute the t-statistic (2-pts)

e) Compute the P-value (2pts) f) At an alpha = 0.05 would you accept or reject the null hypothesis? (3pts)

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

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

Accept