Left-tailed test, variance unknown, 𝛼 = 0.01, n = 23
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\\}."
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