Given a sample size of 35, with sample mean 600 and sample standard deviation 10

Question

Given a sample size of 35, with sample mean 600 and sample standard deviation 100, we

perform the following hypothesis test.

Null Hypothesis H0 : ? = 700

Alternative Hypothesis Ha :? ? 700

17. What is the test statistic?

18. At a 5% significance level (95% confidence level), what is the critical value in this test? Do

we reject the null hypothesis?

19. What are the border values between acceptance and rejection of this hypothesis?

20. What is the power of this test if the assumed true mean were 690 instead of 700?

Please answer all questions and show an explanation.

Explanation / Answer

(17)the test statistic is

Z=(xbar-mu)/(s/vn)

=(600-700)/(100/sqrt(35))

=-5.92

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(18) It is a two-tailed test.

Given a=0.05, the critical value is Z(0.025)=-1.96 or 1.96 (from standard normal table)

Since Z=-5.92 is less than -1.96, we reject the null hypothesis

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(19) The borders are (-1.96, 1.96)

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(20) -1.96 = (xbar-700)/(100/sqrt(35))

--> xbar = 700- 1.96*(100/sqrt(35)) =666.87

So the power is

P(X>666.87) = P((X-mean)/s >(666.87-690)/(100/sqrt(35)))

=P(Z>-1.37)

=0.9147 (from standard normal table)

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