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Chapter 8: Q.117 (page 489)

Insurance companies are interested in knowing the population per cent of drivers who always buckle up before riding in a car.

a. When designing a study to determine this population proportion, what is the minimum number you would need to survey to be 95% confident that the population proportion is estimated to be within 0.03?

b. If it were later determined that it was important to be more than 95% confident and a new survey was commissioned, how would that affect the minimum number you would need to survey? Why?

Short Answer

Expert verified

Part (a) The minimum number you would need to survey to be 95% confident that the population proportion is estimated to be within 0.03is n=1067.11

Part (b) Confidence level also increases as the critical level increases.

Step by step solution

01

Part (a) Explanation

Confidence level for 95%is 伪=0.05

width="106" height="26" role="math">鈬�z0.025=1.96

EBP=0.03estimated proportion within 0.03

p鈥�q鈥�=0.25

Now calculating the sample size, we get,

n=z2p鈥�q鈥�EBP2

鈬�n=1.962脳0.250.032

鈬�n=1067.11

02

Part (b) Explanation

Assuming it was subsequently resolved that it was vital to be over 95%confident and another overview was appointed then the sample size ought to should be more since the critical value increments as the confidence level likewise increments.

Hence, the Confidence level also increases as the critical level increases.

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