Question

Suppose for a study, sample standard deviation s = 5, sample mean xbar = 25 and n = 10. Test the hypothesis that the population mean is different from 24 at 10% significance level.

Answer 1

To test against $H_1:\mu \neq 24$

Here

$\bar{x} = 25, s = 5,n=10$

The test statistic can be written as

$t = \frac{\sqrt{n}(\bar{x}-24)}{s}$ which under H₀ follows a t distribution with n-1 df.

We reject H₀ at 10% level of significance if

Now,

The value of the test statistic $t_{obs}=0.632456$

and critical value

Since $t_{obs}=0.632456 \ngtr t_{0.05,9} = 1.83311$ , so we reject H₀ at 10% level of significance and we can conclude that the population mean is not significantly different from 24.