Question

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

Consider the following hypothesis test.

H₀: μ = 22

H_a: μ ≠ 22

A sample of 75 is used and the population standard deviation is 10. Compute the p-value and state your conclusion for each of the following sample results. Use α = 0.01.

(Round your test statistics to two decimal places and your p-values to four decimal places.)

(a) x = 24

Find the value of the test statistic.

Find the p-value.

p-value =

State your conclusion.

Reject H₀. There is insufficient evidence to conclude that μ ≠ 22.

Reject H₀. There is sufficient evidence to conclude that μ ≠ 22.    

Do not reject H₀. There is sufficient evidence to conclude that μ ≠ 22.

Do not reject H₀. There is insufficient evidence to conclude that μ ≠ 22.

(b) x = 25.2

Find the value of the test statistic.

Find the p-value.

p-value =

State your conclusion.

Reject H₀. There is insufficient evidence to conclude that μ ≠ 22.

Reject H₀. There is sufficient evidence to conclude that μ ≠ 22.    

Do not reject H₀. There is sufficient evidence to conclude that μ ≠ 22.

Do not reject H₀. There is insufficient evidence to conclude that μ ≠ 22.

(c) x = 21

Find the value of the test statistic.

Find the p-value.

p-value =

State your conclusion.

Reject H₀. There is insufficient evidence to conclude that μ ≠ 22.

Reject H₀. There is sufficient evidence to conclude that μ ≠ 22.    

Do not reject H₀. There is sufficient evidence to conclude that μ ≠ 22.

Do not reject H₀. There is insufficient evidence to conclude that μ ≠ 22.

Answer 1

a)

z = (x - mean)/(sigma/sqrt(n))
= (24 - 22)/(10/sqrt(75))
= 1.7321

p value = 0.0833

Do not reject H0. There is insufficient evidence to conclude that μ ≠ 22.

b)

z = (x - mean)/(sigma/sqrt(n))
= (25.2 - 22)/(10/sqrt(75))
= 2.7713

p value = 0.0056

Reject H0. There is sufficient evidence to conclude that μ ≠ 22.

c)

z = (x - mean)/(sigma/sqrt(n))
= (21 - 22)/(10/sqrt(75))
= -0.8660

p value = .3865

Do not reject H0. There is insufficient evidence to conclude that μ ≠ 22.