What critical regions for z would be used to test the hypoth

What critical region(s) for z would be used to test the hypotheses: H_0:=10 versus H_a:10, for = 0.05 ? State the null hypothesis Ho and the alternative hypothesis Ha that would be used for a hypothesis test of the following: The mean age of the students enrolled in evening classes at a certain college is greater than 26 years.

I can do this on a caculator, I need to see the steps broken down please.

Solution

As this is a two tailed test, at alpha = 0.05, then

alpha/2 = 0.05/2 = 0.025

Thus,

zcrit = z(alpha/2) = +/- 1.959963985

Thus, the critical regions are

z < -1.959963985 or z > 1.959963985 [ANSWER, CRITICAL REGION]

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As the claim is that the mean is GREATER than 26 years, then that goes to the alternative hypothesis.

hence,

Ho: u <= 26
Ha: u > 26 [ANSWER, hypotheses]

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