Question

Mimi was curious if regular excise really helps weight loss, hence she decided to perform a hypothesis test. A random sample of 5 students was chosen. The students took a 30- minute exercise every day for 6 months. The weight was recorded for each individual before and after the exercise regimen. Does the data below suggest that the regular exercise helps weight loss? Assume Mimi wants to use a 0.05 significance level to test the claim.

1- Before 190 After 180

2- Before 170 After 160

3- Before 185 After 190

4- Before 160 After 160

5- Before 200 After 190

(a) What is the appropriate hypothesis test to use for this analysis: z-test for two proportions, t-test for two proportions, t-test for two dependent samples (matched pairs), or t-test for two independent samples? Please identify and explain why it is appropriate.

(b) Let μ1 = mean weight before the exercise regime. Let μ2 = mean weight after the exercise regime. Which of the following statements correctly defines the null hypothesis?

(i) μ1 - μ2 > 0 (μd > 0)

(ii) μ1 - μ2 = 0 (μd = 0)

(iii) μ1 - μ2 < 0 (μd < 0)

Answer 1

a)

t-test for two dependent samples (matched pairs)

b)

(ii) μ1 - μ2 > 0 (μd > 0)

Before    after   dbar
1901   180   1721
170   160   10
185   190   -5
160   160   0
200   190   10

dbar = μ(before) - μ(after) = 347.2
s(dbar) = 768.01

SE = s(dbar)/sqrt(n)  
= 168.01/sqrt(5)
=343.4623

Test Statisitcs,

t = dbar/SE  
= 347.2/342.4623
= 1.011

p value = 0.1846

Do not reject H0 as p value > 0.05