H_0: mu = 25 H_a: mu notequalto 25 x = 28.3, n = 59, sigma = 8.47, alpha = .01 a

Question

H_0: mu = 25 H_a: mu notequalto 25 x = 28.3, n = 59, sigma = 8.47, alpha = .01 a. Use the data given to test the following hypotheses. (Round your answer to 2 decimal places.) The value of the test statistic is and we reject null hypothesis. b. Use the p-value to reach a statistical conclusion. (Round your answer to 4 decimal places.) Since the p-value of is less than a/2 = .005, the decision is to: Reject the null hypothesis c. Using the critical value method, what are the critical sample mean values? Upper value: Lower value:

Explanation / Answer

a] H0: =25 vs Ha: is not equal to 25

Xbar = 28.3 , n= 59 , = 8.47 alpha = 0.01

Test statistic = (Xbar - ) / ( /sqrt(n))

t = (28.3-25) / (8.47/sqrt(59))

t = 3.3 / 1.1027

test statistic = 2.9926

Z calc = Z0.01/2 =Z 0.005 = 2.58

so we reject the null hypothesis.

b] p-value = P(Ztable = 2.58 > Z calc = 2.9926)

p-value = 0.0028 < alpha = 0.01

so, we reject H0.

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