Question

Test the hypothesis for the mean is 5 versus the mean is less than 5 with the following summary statistics

n = 100, stand dev = 3.678 and mean = 4.530

please show work

Answer 1

The test statistic here is computed as:

As this is a one tailed lower tailed test, the p-value here is computed from the t distribution tables for n - 1 = 99 degrees of freedom as:

p = P( t₉₉< - 1.2779 ) = 0.1021

Therefore the p-value here is 0.1021

Assuming the level of significance as 0.05, we see that the p-value here is 0.1021 > 0.05 which is the level of significance, therefore the test is not significant and we cannot reject the null hypothesis here. Therefore we dont have sufficient evidence to support the claim that the mean is less than 5.