QUESTIONS

Question 1

A police officer claims that the proportion of drivers wearing seat belts is more than 55%. To test this claim, a random sample of drivers are checked for seat belt usage.

Assume that the test statistic for this hypothesis test is 1.87.

Assume the critical value for this hypothesis test is 1.645.

Come to a decision for the hypothesis test and interpret your results with respect to the original claim.

Fail to reject the null hypothesis.
There is not enough evidence to support the claim that the proportion of drivers wearing seat belts is more than 55%.
Reject the null hypothesis.
There is enough evidence to support the claim that the proportion of drivers wearing seat belts is more than 55%.

Question 2

An aspiring venture capitalist is interested in studying early-stage companies. She claims that the proportion of new businesses that earn a profit within the first two years of operation is more than 18%. If the venture capitalist chooses a 10% significance level, what is/are the critical value(s) for the hypothesis test?

Z0.10	Z0.05	Z0.025	Z0.01	Z0.005
1.282	1.645	1.960	2.326	2.576

Use the curve below to show your answer. Select the appropriate test by dragging the blue point to a right-, left- or two-tailed diagram. The shaded area represents the rejection region. Then, set the critical value(s) on the x-axis by moving the slider.

Question 3

An economist is interested in studying unemployment. He claims that the proportion of people who are unemployed for more than six months is not 20%. If the economist chooses a 1% significance level, what is/are the critical value(s) for the hypothesis test?

z0.10	z0.05	z0.025	z0.01	z0.005
1.282	1.645	1.960	2.326	2.576

Question 4

Based the results from the school psychologist’s investigation of the proportion of questions that are related to cultural sensitivity on the aptitude test, choose the correct conclusion that interprets the results within the context of the hypothesis test.

There is NOT sufficient evidence that the proportion of questions related to cultural sensitivity is less than 25%.
There is sufficient evidence that the proportion of questions related to cultural sensitivity is less than 25%.
There is sufficient evidence that the proportion of questions related to cultural sensitivity is less than 50%.
There is NOT sufficient evidence that the proportion of questions related to cultural sensitivity is less than 50%.

Question 5

A school psychologist would like to investigate whether an aptitude test includes less than 25% questions that are related to cultural sensitivity. Based on the following results, conclude whether to reject or not reject H0.

H0: p=0.25; Ha: p<0.25
α=0.01(significance level)
The test statistic is −1.30.
The critical value is z₀₁= −2.33.

Select two responses below.

Fail to reject H0.
Reject H0.
The test statistic is NOT in the rejection region.
The test statistic falls within the rejection region.

Question 6

A psychologist is interested in studying the sleeping patterns of individuals diagnosed with depression. She claims that the proportion of depressed patients who sleep 8 hours per night is less than 75%. If the psychologist chooses a 0.5% significance level, what is/are the critical value(s) for the hypothesis test?

z0.10	z0.05	z0.025	z0.01	z0.005
1.282	1.645	1.960	2.326	2.576

Question 7

A social media manager for a growing startup claims that exactly 55% of all online sales are made through the company’s ads on social media, which draw new customers to the online store. If the social media manager chooses a 10% significance level, what is/are the critical value(s) for this two-tailed hypothesis test (Ha: p≠p0)?

Round your answer to 3 decimal places.

z_0.10	z_0.05	z_0.025	z_0.01	z_0.005
1.282	1.645	1.960	2.326	2.576

Enter the smaller critical value first and the larger critical value second in the answer boxes.

Question 8

A store owner claims that the proportion of accurate scans of the bar coding system is greater than 95%. To test this claim, a random sample of store transactions are monitored and checked for scanning accuracy.

Assume that the test statistic for this hypothesis test is 1.16.

Assume the critical value for this hypothesis test is 1.282.

Come to a decision for the hypothesis test and interpret your results with respect to the original claim.

Reject the null hypothesis.
There is enough evidence to support the claim that the proportion of accurate scans of the bar coding system is greater than 95%.
Fail to reject the null hypothesis.
There is not enough evidence to support the claim that the proportion of accurate scans of the bar coding system is greater than 95%.

Question 9

Based on Hope’s results regarding the proportion of hospital acquired pressure ulcers (HAPUs) occurring in restrained ICU patients is different than those unrestrained at 50%, choose the correct conclusion that interprets the results within the context of the hypothesis test.

There is sufficient evidence that the proportion of hospital acquired pressure ulcers (HAPUs) occurring in restrained ICU patients is different than those unrestrained at 50%.
There is NOT sufficient evidence that the proportion of hospital acquired pressure ulcers (HAPUs) occurring in restrained ICU patients is different than those unrestrained at 50%.
There is sufficient evidence that the proportion of hospital acquired pressure ulcers (HAPUs) occurring in restrained ICU patients is different than those unrestrained at 25%.
There is NOT sufficient evidence that the proportion of hospital acquired pressure ulcers (HAPUs) occurring in restrained ICU patients is different than those unrestrained at 25%.

Question 10

Hope, an ICU nurse, predicts that proportion of hospital acquired pressure ulcers (HAPUs) occurring among restrained ICU patients is different than those unrestrained at 50%. Based on this information and the information below, conclude whether to reject or not reject H0.

H0 : p=0.50; Ha: p≠0.50
α=0.05(significance level)
The test statistic is 01.
The critical value is z₀₂₅=−1.96,1.96.

Select two responses below.

Reject H0.

Fail to reject H0.

The test statistic falls within the rejection region.

The test statistic is NOT in the rejection region.

ANSWERS:

Question 1

A police officer claims that the proportion of drivers wearing seat belts is more than 55%. To test this claim, a random sample of drivers are checked for seat belt usage.

Assume that the test statistic for this hypothesis test is 1.87.

Assume the critical value for this hypothesis test is 1.645.

Come to a decision for the hypothesis test and interpret your results with respect to the original claim.

Fail to reject the null hypothesis.
There is not enough evidence to support the claim that the proportion of drivers wearing seat belts is more than 55%.
Reject the null hypothesis.
There is enough evidence to support the claim that the proportion of drivers wearing seat belts is more than 55%.

Answer

Reject the null hypothesis.
There is enough evidence to support the claim that the proportion of drivers wearing seat belts is more than 55%.

Question 2

Z0.10	Z0.05	Z0.025	Z0.01	Z0.005
1.282	1.645	1.960	2.326	2.576

Answer

[Graph]

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(Answer) MATH399N – Week 7 Assignment: Conduct a Hypothesis Test for Proportion – Critical Value/Rejection Region Approach