Question

In a survey of 1000 drivers from Region​ A, 869 wear a seat belt. In a survey of 1000 drivers from Region​ B, 916 wear a seat belt. At alphaequals0.05​, 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 and Upper H Subscript a.

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 proportion of drivers who wear seat belts in Region A is greater than the proportion of drivers who wear seat belts in Region B.

B. The claim is that the proportions of drivers who wear seat belts in both regions are equal.

C. 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.

D. The claim is that the proportions of drivers who wear seat belts in both regions add up to 1.

State Upper H 0 and Upper H Subscript a. Choose the correct answer below.

A. Upper H 0​: p 1not equalsp 2 Upper H Subscript a​: p 1equalsp 2

B. Upper H 0​: p 1less than or equalsp 2 Upper H Subscript a​: p 1greater thanp 2

C. Upper H 0​: p 1greater than or equalsp 2 Upper H Subscript a​: p 1less thanp 2

D. Upper H 0​: p 1greater thanp 2 Upper H Subscript a​: p 1less than or equalsp 2

E. Upper H 0​: p 1equalsp 2 Upper H Subscript a​: p 1not equalsp 2

F. Upper H 0​: p 1less thanp 2 Upper H Subscript a​: p 1greater than or equalsp 2

​(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 0equals = ​, and two rejection​ regions, zless than = and zgreater than =   ​(Use a comma to separate answers as needed. Round to two decimal places as​ needed.)

B. There is one critical​ value, z 0equals = ​, and one rejection​ region, zgreater than = . ​(Round to two decimal places as​ needed.)

C. There is one critical​ value, z 0equals = ​, and one rejection​ region, zless than = . ​(Round to two decimal places as​ needed.)

​(c) Find the standardized test​ statistic, z. zequals =   ​(Round to two decimal places as​ needed.) ​

(d) Decide whether to reject or fail to reject the null hypothesis.

Since z=  (is not, is) in the rejection​ region(s),=   (reject, fail to reject) Upper H 0.

​(e) Interpret the decision in the context of the original claim. There =  (is not,is) enough evidence at the alphaequals0.05 level of significance to support the claim that the proportion of drivers who wear seat belts in Region A is =  (greater than ,equal to ,not equal to ,less than) the proportion of drivers who wear seat belts in Region B. Click to select your answer(s).

Answer 1

To test the claim we will use z distribution or say Z test.