Consider the following hypothesis test.

H₀: μ ≤ 12

H_a: μ > 12

A sample of 25 provided a sample mean

x = 14

and a sample standard deviation

s = 4.57.

(a)

Compute the value of the test statistic. (Round your answer tothree decimal places.)

(b)

Use the t distribution table to compute a range for thep-value.

p-value > 0.2000.100 < p-value <0.200    0.050 < p-value <0.1000.025 < p-value < 0.0500.010 <p-value < 0.025p-value < 0.010

(c)

At

α = 0.05,

what is your conclusion?

Do not reject H₀. There is sufficientevidence to conclude that μ > 12.Do not rejectH₀. There is insufficient evidence to concludethat μ > 12.    RejectH₀. There is insufficient evidence to concludethat μ > 12.Reject H₀. There is sufficientevidence to conclude that μ > 12.

(d)

What is the rejection rule using the critical value? (If thetest is one-tailed, enter NONE for the unused tail. Round youranswer to three decimal places.)

test statistic≤test statistic≥

What is your conclusion?

Do not reject H₀. There is sufficientevidence to conclude that μ > 12.Do not rejectH₀. There is insufficient evidence to concludethat μ > 12.    RejectH₀. There is insufficient evidence to concludethat μ > 12.Reject H₀. There is sufficientevidence to conclude that μ > 12.