Question

  

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Consider the following hypothesis test.

H0: μ ≥ 70

Ha: μ < 70

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 = 68.5

Find the value of the test statistic.

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

p-value =

State your conclusion.

Do not reject H₀. There is insufficient evidence to conclude that μ < 70.

Do not reject H₀. There is sufficient evidence to conclude that μ < 70.   

Reject H₀. There is insufficient evidence to conclude that μ < 70.

Reject H₀. There is sufficient evidence to conclude that μ < 70.

(b) x = 67

Find the value of the test statistic.

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

p-value =

State your conclusion.

Do not reject H₀. There is insufficient evidence to conclude that μ < 70.

Do not reject H₀. There is sufficient evidence to conclude that μ < 70.    

Reject H₀. There is insufficient evidence to conclude that μ < 70.

Reject H₀. There is sufficient evidence to conclude that μ < 70.

(c) x = 65.5

Find the value of the test statistic.

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

p-value =

State your conclusion.

Do not reject H₀. There is insufficient evidence to conclude that μ < 70.

Do not reject H₀. There is sufficient evidence to conclude that μ < 70.    

Reject H₀. There is insufficient evidence to conclude that μ < 70.

Reject H₀. There is sufficient evidence to conclude that μ < 70.

(d) x = 73.5

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.

Do not reject H₀. There is insufficient evidence to conclude that μ < 70.

Do not reject H₀. There is sufficient evidence to conclude that μ < 70.   

Reject H₀. There is insufficient evidence to conclude that μ < 70.

Reject H₀. There is sufficient evidence to conclude that μ < 70.

Answer 1

Part a)

Test Statistic :-


Z = -1.25

Test Criteria :-
Reject null hypothesis if


Result :- Fail to reject null hypothesis

P value = P ( Z < -1.25 ) = 0.1056

Reject null hypothesis if P value <    level of significance
P - value = 0.1056 > 0.01 ,hence we fail to reject null hypothesis
Conclusion :- Fail to reject null hypothesis

Do not reject H₀. There is insufficient evidence to conclude that μ < 70.

part b)

Test Statistic :-


Z = -2.5

P value = P ( Z < -2.5 ) = 0.0062

Reject null hypothesis if P value <    level of significance
P - value = 0.0062 < 0.01 ,hence we reject null hypothesis
Conclusion :- Reject null hypothesis

Reject H₀. There is sufficient evidence to conclude that μ < 70.

Part c)

Test Statistic :-


Z = -3.75

P value = P ( Z < -3.75 ) = 0.0001

Reject null hypothesis if P value <    level of significance
P - value = 0.0001 < 0.01 ,hence we reject null hypothesis
Conclusion :- Reject null hypothesis

Reject H₀. There is sufficient evidence to conclude that μ < 70.

Part d)

Test Statistic :-


Z = 2.92

P value = P ( Z < 2.92 ) = 0.9982

Reject null hypothesis if P value <    level of significance
P - value = 0.9982 > 0.01 ,hence we fail to reject null hypothesis
Conclusion :- Fail to reject null hypothesis

Do not reject H₀. There is insufficient evidence to conclude that μ < 70.