Question

Consider the following hypothesis test.

H0: μ ≤ 50

Ha: μ > 50

A sample of 60 is used and the population standard deviation is 8. Use the critical value approach to state your conclusion for each of the following sample results. Use α = 0.05.

(Round your answers to two decimal places.)

(a) x = 52.7 Find the value of the test statistic.

State the critical values for the rejection rule. (If the test is one-tailed, enter NONE for the unused tail.)

test statistic ≤_______

test statistic ≥_______

State your conclusion.

Reject H₀. There is insufficient evidence to conclude that μ > 50.

Do not reject H₀. There is sufficient evidence to conclude that μ > 50.     

Do not reject H₀. There is insufficient evidence to conclude that μ > 50.

Reject H₀. There is sufficient evidence to conclude that μ > 50.

(b) x = 51

Find the value of the test statistic. _____

State the critical values for the rejection rule. (If the test is one-tailed, enter NONE for the unused tail.)

test statistic ≤ _____

test statistic ≥ _____

State your conclusion.

Reject H₀. There is insufficient evidence to conclude that μ > 50.

Do not reject H₀. There is sufficient evidence to conclude that μ > 50.     

Do not reject H₀. There is insufficient evidence to conclude that μ > 50.

Reject H₀. There is sufficient evidence to conclude that μ > 50.

(c) x = 51.9

Find the value of the test statistic.

State the critical values for the rejection rule. (If the test is one-tailed, enter NONE for the unused tail.)

test statistic ≤ _____

test statistic ≥ _____

State your conclusion.

Reject H₀. There is insufficient evidence to conclude that μ > 50.

Do not reject H₀. There is sufficient evidence to conclude that μ > 50.     

Do not reject H₀. There is insufficient evidence to conclude that μ > 50.

Reject H₀. There is sufficient evidence to conclude that μ > 50.

Answer 1