Question

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Consider the following hypothesis test.

H₀: μ ≥ 80

H_a: μ < 80

A sample of 100 is used and the population standard deviation is 12. Compute the p-value and state your conclusion for each of the following sample results. Use α = 0.01.

(a) x = 78.5,    Find the value of the test statistic.

?

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

p-value = ?

State your conclusion.

a) Reject H₀. There is insufficient evidence to conclude that μ < 80.

b) Reject H₀. There is sufficient evidence to conclude that μ < 80.   

c) Do not reject H₀. There is sufficient evidence to conclude that μ < 80.

d) Do not reject H₀. There is insufficient evidence to conclude that μ < 80.

(b) x = 77, Find the value of the test statistic.

?

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

p-value = ?

State your conclusion.

a) Reject H₀. There is insufficient evidence to conclude that μ < 80.

d) Reject H₀. There is sufficient evidence to conclude that μ < 80.    

c) Do not reject H₀. There is sufficient evidence to conclude that μ < 80.

d) Do not reject H₀. There is insufficient evidence to conclude that μ < 80.

(c) x = 75.5, Find the value of the test statistic.

?

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

p-value = ?

State your conclusion.

a) Reject H₀. There is insufficient evidence to conclude that μ < 80.

b) Reject H₀. There is sufficient evidence to conclude that μ < 80.   

c) Do not reject H₀. There is sufficient evidence to conclude that μ < 80.

d) Do not reject H₀. There is insufficient evidence to conclude that μ < 80.

(d) x = 83.5, Find the value of the test statistic. (Round your answer to two decimal places.)

?

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

p-value = ?

State your conclusion.

a) Reject H₀. There is insufficient evidence to conclude that μ < 80.

b) Reject H₀. There is sufficient evidence to conclude that μ < 80.    

c) Do not reject H₀. There is sufficient evidence to conclude that μ < 80.

d) Do not reject H₀. There is insufficient evidence to conclude that μ < 80.

Answer 1