Question

1. A psychological test inventory called POMS was given to a sample of 25 runners. The result showed that the mean was 10.46 with standard deviation of 5.55. A psychologist suspected that, in general, runners have a mean score on POMS that is different from the national norm of 13. (a) At α=1%, using the classical approach to test the claim. (b) Using P-value approach to conclude it.

Answer 1

Here claim is that mean value is different from 13

So hypothesis here is vs

Let us assume that distribution is normal, as n<30 and standard deviation not known so we will use t test statistics

a. The t-critical values for a two-tailed test, for a significance level of α=0.01 are

tc​=−2.797 and tc​=2.797

Graphically

As test statistics do not fall in the rejection region, we fail to reject the null hypothesis

b. P value is TDIST(2.29,24,2)=0.0311

As P value is greater than alpha=0.01, we fail to reject the null hypothesis

Hence we do not have sufficient evidence to support the claim that mean is different from 13