Question

In a survey of 1000 1000 drivers from Region​ A, 848 848 wear a seat belt. In a survey of 1000 1000 drivers from Region​ B, 906 906 wear a seat belt. At alpha α equals = 0.10 0.10​, is there evidence to support the claim that the proportion of drivers who wear seat belts in Region A is less than the proportion of drivers who wear seat belts in Region​ B? Assume that the samples are random and independent. Complete parts​ (a) through​ (e) below. ​(a) Identify the claim and state Upper H 0 H0 and Upper H Subscript a Ha. Identify the claim. Let population 1 be drivers from Region A and let population 2 be drivers from Region B. Choose the correct answer below. A. The claim is that the proportions of drivers who wear seat belts in both regions add up to 1. B. The claim is that the proportion of drivers who wear seat belts in Region A is less than the proportion of drivers who wear seat belts in Region B. C. The claim is that the proportions of drivers who wear seat belts in both regions are equal. D. The claim is that the proportion of drivers who wear seat belts in Region A is greater than the proportion of drivers who wear seat belts in Region B. State Upper H 0 H0 and Upper H Subscript a Ha. Choose the correct answer below. A. Upper H 0 H0​: p 1 p1 greater than > p 2 p2 Upper H Subscript a Ha​: p 1 p1 less than or equals ≤ p 2 p2 B. Upper H 0 H0​: p 1 p1 equals = p 2 p2 Upper H Subscript a Ha​: p 1 p1 not equals ≠ p 2 p2 C. Upper H 0 H0​: p 1 p1 less than or equals ≤ p 2 p2 Upper H Subscript a Ha​: p 1 p1 greater than > p 2 p2 D. Upper H 0 H0​: p 1 p1 less than < p 2 p2 Upper H Subscript a Ha​: p 1 p1 greater than or equals ≥ p 2 p2 E. Upper H 0 H0​: p 1 p1 not equals ≠ p 2 p2 Upper H Subscript a Ha​: p 1 p1 equals = p 2 p2 F. Upper H 0 H0​: p 1 p1 greater than or equals ≥ p 2 p2 Upper H Subscript a Ha​: p 1 p1 less than < p 2 p2 ​(b) Find the critical​ value(s) and identify the rejection​ region(s). Select the correct choice below and fill in the answer boxes to complete your choice. A. There are two critical​ values, z 0 z0 equals = nothing ​, and two rejection​ regions, z less than < nothing and z greater than > nothing . ​(Use a comma to separate answers as needed. Round to two decimal places as​ needed.) B. There is one critical​ value, z 0 z0 equals = nothing ​, and one rejection​ region, z greater than > nothing . ​(Round to two decimal places as​ needed.) C. There is one critical​ value, z 0 z0 equals = nothing ​, and one rejection​ region, z less than < nothing . ​(Round to two decimal places as​ needed.) ​(c) Find the standardized test​ statistic, z. z equals = nothing ​(Round to two decimal places as​ needed.) ​(d) Decide whether to reject or fail to reject the null hypothesis. Since z ▼ is is not in the rejection​ region(s), ▼ reject fail to reject Upper H 0 H0. ​(e) Interpret the decision in the context of the original claim. There ▼ is not is enough evidence at the alpha α equals = 0.10 0.10 level of significance to support the claim that the proportion of drivers who wear seat belts in Region A is ▼ equal to less than not equal to greater than the proportion of drivers who wear seat belts in Region B.

Answer 1