Question

A sample of 71 observations is selected from a normal population. The sample mean is 24, and the population standard deviation is 8.

Conduct the following test of hypothesis using the 0.05 significance level.

H₀ : μ ≤ 23

H₁ : μ > 23

a. Is this a one- or two-tailed test?

(Click to select)  One-tailed test  Two-tailed test

b. What is the decision rule? (Round the final answer to 3 decimal places.)

(Click to select)  Reject  Accept  H₀ and  (Click to select)  accept  reject  H₁ when z >  .

c. What is the value of the test statistic? (Round the final answer to 2 decimal places.)

Value of the test statistic

d. What is your decision regarding H₀?

(Click to select)  Do not reject  Reject  H₀.

There is  (Click to select)  enough  not enough   evidence to conclude that the population mean is greater than 23.

e. What is the p-value? (Round the final answer to 4 decimal places.)

Answer 1

a) As we are testing here whether the mean is greater than 23, therefore this is a one tailed test here. ( as we are only testing it from the up side)

b) For 0.05 level of significance, we have from the standard normal tables:
P( Z < 1.645) = 0.95

Therefore, P(Z > 1.645) = 0.05

Therefore 0.05 is the required critical value here.

The decision rule therefore is given here as:
Reject H0 if z > 1.645

c) The test statistic value now is computed here as:

Therefore 1.0533 is the required test statistic value here.

d) As the test statistic value here is less than the critical value, the test is not significant and we cannot reject the null hypothesis here. Therefore Do no reject the H0 is the correct decision here.

e) The p-value from the standard normal tables, is computed here as:

p = P(Z > 1.0533) = 0.146

Therefore 0.1460 is the required p-value here.