Solution. We define null and alternative hypothesis:
Next we find a critical value. We will use a right-tailed test, for which a t-test for one mean, with unknown population standard deviation will be used.
The significance level is , and the critical value for a right-tailed test is
The rejection region for this right-tailed test is .
The t-statistic is computed as follows:
Since it is observed that , it is then concluded that the null hypothesis is rejected.
Conclusion:
It is concluded that the null hypothesis is rejected. Therefore, there is enough evidence to claim that the population mean is greater than 25, at the 0.05 significance level.
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