Question

Surprisingly, a study found that children under stress reported fewer symptoms of depression and anxiety but scored higher on a Lie Scale (a measure of tendency to give socially desirable responses). The population mean for the Lie Scale for nonstressed children is 3.8. A sample of 40 children under stress had Lie Scale sample mean of 4.4, with a standard deviation of 2.5. Test the hypothesis that children under stress are more likely to give socially desirable answers. Write a complete conclusion in the context of the problem.

Answer 1

Solution:

Given:

From the data, sample mean is = 4.4 and the Sample standard deviation is s = 2.4, and the sample size is n = 40.

Null and Alternative Hypotheses:

This corresponds to a two-tail test, for which a t-test for one mean, with unknown population standard deviation will be used.

Test statistic:

The number of degrees of freedom are df = n-1 = 40-1=39

Rejection Region:
Given significance level = α = 0.05 and df = 39
So Critical Value for the test is, tc = 1.685   ...Using t-table

Decision:

Since it is observed that t = 1.518 < tc = 3.055
It is then concluded that the Null Hypothesis is not rejected.

Conclusion: It is concluded that the Null Hypothesis is not rejected. Therefore, there is not enough evidence to claim that children under stress are more likely to give socially desirable answers at the 0.05 significance level.

Done