Question

We wish to test H0: μ = 120 versus Ha: μ ¹ 120, where ? is known to equal 14. The sample of n = 36 measurements randomly selected from the population has a mean of ?̅ = 15.

a. Calculate the value of the test statistic z.

b. By comparing z with a critical value, test H0 versus Ha at ? = .05.

Answer 1

It is a two tailed hypothesis test

with hypotheses

(A) test statistic =

setting the given values

we get

(B) using z critical value, we get z critical values = -1.96 and 1.96 (using z table for alpha= 0.05)

We can see that z statistic is falling outside the z critical region of -1.96 to 1.96

therefore, we can reject the null hypothesis and we can say that there is sufficient evidence to conclude that the mean is significantly different from 20