Question

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

Consider the following hypothesis test.

H₀: μ ≤ 25

H_a: 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

The statistic software output for this problem is:

(a)

Test statistics = 1.69

(b)

P-value = 0.0458

(c)

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

(d)

Critical value = 2.33

test statistic ≤ 2.33

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