Answer to Question #350449 in Statistics and Probability for barbie

Question

Hypothesis test on population mean; 𝛼 = 0.05; one-tailed test (right); 𝑛 = 37; 𝑠 = 5

Answer 1

This corresponds to a right-tailed test, for which a t-test for one mean, with unknown population standard deviation, using the sample standard deviation, will be used.

Based on the information provided, the significance level is $\alpha = 0.05,$ $df=n-1=36$ and the critical value for a right-tailed test is $t_c =1.6882985.$

The rejection region for this right-tailed test is $R = \{t:t>1.688298\}.$

The t-statistic is computed as follows:

$$t=\dfrac{\bar{x}-\mu}{s/\sqrt{n}}$$

If $t>1.688298=t_c,$ the null hypothesis is rejected.