Question

What statistical test should be used for the following study? A corporation psychologist believes that exercise affects self-image. To investigate this possibility, 14 employees of the corporation are randomly selected to participate in a jogging program. Before beginning the program, they are given a questionnaire that measures self-image. Then they begin the jogging program. The program consists of jogging at a moderately taxing rate for 20 minutes a day, 4 days a week. Each employee's self-image is measured again after 2 months on the program.

Answer 1

Related samples –Paired t-test

Because n<30 i.e Sample size is less than 30.

Sample sizes are equal. n1=n2 =14=n

That is we are making two observations one before joining jogging program and another after 2 months of joining jogging program on the same individual.

Paired – t –test:
Let di = Xi – Yi (i = 1, 2, ……n) denote the difference in the observations for the ith unit.
Null hypothesis:
H0 : μ1 = μ2 ( Exercise doesn't affect self-image)
Alternative Hypothesis:
H1 : μ1 ≠ μ2 (μ1 > μ2 (or) μ1 < μ2) ( Exercise affects self-image)

Calculation of test statistic:
t =  

where = / n

and =

Expected value :

te ( From t-distribution table)

follows t- distribution with n-1 degrees of freedom.

Inference:
By comparing t0 and te at the desired level of significance, usually 5% or 1%, we
reject or accept the null hypothesis.