Question

A colleague of the investigators is problem 3 repeats the experiment but matches the samples on the dimensions of sex and job type. the raw data appear below. Evaluate her experiment using the criteria of p < .05. Assume it is a two tailed test.

Pairs: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Contr: 38 40 35 36 35 32 31 30 28 26 24 21 18 34 22

Relax: 35 32 30 34 30 32 28 27 22 22 18 17 17 25 21

Answer 1

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho: μD​ = 0

Ha: μD​ ≠ 0

This corresponds to a two-tailed test, for which a t-test for two paired samples be used.

(2) Rejection Region

Based on the information provided, the significance level is α=0.05, and the degrees of freedom are df=14.

Hence, it is found that the critical value for this two-tailed test is tc​=2.145, for α=0.05 and df=14.

The rejection region for this two-tailed test is R={t:∣t∣>2.145}.

(3) Test Statistics

The t-statistic is computed as shown in the following formula:

(4) Decision about the null hypothesis

Since it is observed that ∣t∣=6.043>tc​=2.145, it is then concluded that the null hypothesis is rejected.

Using the P-value approach: The p-value is p=0, and since p=0.000<0.05, it is concluded that the null hypothesis is rejected.

(5) Conclusion: It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that population mean μ1​is different than μ2​, at the 0.05 significance level.