Question

Consider the following hypothesis test

H0 : µ ? 12

Ha : µ > 12

A sample of 25 provided a sample mean x= 14 and a sample standard deviation s = 4.32

a. what is the value of the test statistic?

b. At ? = 0.05, what is your conclusion ?

Answer 1

a) The test statistic here is computed as:

Therefore 2.3148 is the test statistic value here.

b) For n -1 = 24 degrees of freedom, we get from the t distribution tables as:

p = P( t₂₄ > 2.3148 ) = 0.0147

As this is a one tailed test, and p-value here is 0.0147 < 0.05 which is the level of significance, therefore the test is significant and we can reject the null hypothesis here and conclude that we have suddicient evidence for mean being greater than 12.