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**

reject or accept the null hypothesis.

PAIRED SAMPLES T TEST A Corporation Psychologist believes that
exercise affects self-image. To investigate this probability, 14
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jogging program. They jogged 4 days a week for 20 minutes. Each
employee’s self-image is measured again after two months on the
program. The results are as follows: the higher the score, the
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