Answer to Question #342813 in Statistics and Probability for Michele

Question

Left-tailed test, variance unknown, 𝛼 = 0.01, n = 23

Answer 1

The following null and alternative hypotheses need to be tested:

$H_0:\mu\ge\mu_0$

$H_a:\mu<\mu_0$

This corresponds to a left-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 $\alpha = 0.01,$ $df=n-1=22$ degrees of freedom, and the critical value for a left-tailed test is $t_c =-2.508325.$The rejection region for this left-tailed test is $R = \{t:t<-2.508325\}.$