Question

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 = 4.64.

(a)

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

(b)

Use the t distribution table to compute a range for the p-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 sufficient evidence to conclude that μ > 12.Reject H₀. There is insufficient evidence to conclude that μ > 12.    Reject H₀. There is sufficient evidence to conclude that μ > 12.Do not reject H₀. There is insufficient evidence to conclude that μ > 12.

(d)

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

test statistic≤test statistic≥

What is your conclusion?

Do not reject H₀. There is sufficient evidence to conclude that μ > 12.Reject H₀. There is insufficient evidence to conclude that μ > 12.    Reject H₀. There is sufficient evidence to conclude that μ > 12.Do not reject H₀. There is insufficient evidence to conclude that μ > 12.

Answer 1

(a)

(b)

Using t table,

0.010 < p-value < 0.025

(c)

Reject H0. There is sufficient evidence to conclude that μ > 12.

(d)

Reject H0. There is sufficient evidence to conclude that μ > 12.

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