Question

You may need to use the appropriate appendix table or technology to answer this question.

Consider the following hypothesis test.

H0: μ ≤ 25

Ha: μ > 25

A sample of 40 provided a sample mean of 26.6. The population standard deviation is 6.

(a)

Find the value of the test statistic. (Round your answer to two decimal places.)

(b)

Find the p-value. (Round your answer to four decimal places.)

p-value =

(c)

At

α = 0.01,

state your conclusion.

Reject H₀. There is sufficient evidence to conclude that μ > 25.

Reject H₀. There is insufficient evidence to conclude that μ > 25.     

Do not reject H₀. There is sufficient evidence to conclude that μ > 25.

Do not reject H₀. There is insufficient evidence to conclude that μ > 25.

(d)

State the critical values for the rejection rule. (Round your answer to two decimal places. If the test is one-tailed, enter NONE for the unused tail.)

test statistic≤test statistic≥

State your conclusion.

Reject H₀. There is sufficient evidence to conclude that μ > 25.

Reject H₀. There is insufficient evidence to conclude that μ > 25.     

Do not reject H₀. There is sufficient evidence to conclude that μ > 25.

Do not reject H₀. There is insufficient evidence to conclude that μ > 25.

Answer 1

solution:

population standard deviation

This corresponds to a right-tailed test, for which a z-test for one mean, with known population standard deviation will be used.

he significance level is

the critical value for a right-tailed test is

a) test statistics:

b) p value = 1 - value of z to the left of 1.69 = 0.9545

The p-value is p=0.0455

(the p value is calculated from the z table to the right of 1.69)

c) Conclusion

since p = 0.0455 > so,

at do not reject H0 : there is insufficient evidance to conclude that .

d) Since it is observed that z=1.687 ≤ zc= 2.33

so do not reject the H0 : there is insufficient evidance to conclude that .