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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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Most popular questions from this chapter

On May 23,2013, Gallup reported that of the 1005people surveyed, 76%of U.S. workers believe that they will continue working past retirement age. The confidence level for this study was reported at 95%with a 卤3%margin of error.

a. Determine the estimated proportion from the sample.

b. Determine the sample size.

c. Identify CL and .

d. Calculate the error bound based on the information provided.

e. Compare the error bound in part d to the margin of error reported by Gallup. Explain any differences between the values.

f. Create a confidence interval for the results of this study.

g. A reporter is covering the release of this study for a local news station. How should she explain the confidence interval to her audience?

Define the random variable X in words.

A pharmaceutical company makes tranquilizers. It is assumed that the distribution for the length of time they last is

approximately normal. Researchers in a hospital used the drug on a random sample of nine patients. The effective period of

the tranquilizer for each patient (in hours) was as follows: 2.7;2.8;3.0;2.3;2.3;2.2;2.8;2.1;and2.4.

a.i.x虅=__________ii.sx=__________iii.n=__________iv.n鈥�1=__________

b. Define the random variable Xin words.

c. Define the random variable Xin words.

d. Which distribution should you use for this problem? Explain your choice.

e. Construct a 95%confidence interval for the population mean length of time.

i. State the confidence interval.

ii. Sketch the graph.

iii. Calculate the error bound.

f. What does it mean to be 鈥�95% confident鈥� in this problem?

State the estimated distribution of P鈥�.Construct a 92%Confidence Interval for the true proportion of girls in the ages 8to12beginning ice-skating classes at the Ice Chalet.

In words, define the random variable X.
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