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Chapter 8: Q.45 (page 497)

Election polling Gloria Chavez and Ronald Flynn are the candidates for mayor in a large city. We want to estimate the proportion pof all registered voters in the city who plan to vote for Chavez with 95% confidence and a margin of error no greater than 0.03. How large a random sample do we need? Show your work.

Short Answer

Expert verified

From the given information, the sample size of the registered voter is1068

Step by step solution

01

Given Information

It is given in the question, the margin of errorE=0.03

confidence interval95%

How large a random sample do we need?

02

Explanation

Confidence interval is 95%

Convert 95%into decimal.

95100=0.95

For confidence interval 0.95,use table A.

zα/2=1.96

Since the sample proportion p∧is unknown.

Calculate sample size. Use the formula n=[zα/2]2×0.25E2

n=[zα/2]2×0.25E2

n=1.962×0.250.032

=1068

Hence, the required sample size is1068.

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Most popular questions from this chapter

A radio talk show host with a large audience is interested in the proportion pof adults in his listening area who think the drinking age should be lowered to eighteen. To find this out, he poses the following question to his listeners: "Do you think that the drinking age should be reduced to eighteen in light of the fact that eighteen-year-olds are eligible for military service?" He asks listeners to phone in and vote "Yes" if they agree the drinking age should be lowered and "No" if not. Of the 100people who phoned in, 70answered "Yes." Which of the following conditions for inference about a proportion using a confidence interval are violated?

I. The data are a random sample from the population of interest.

II. nis so large that both np⏞andn1-p⏞are at least 10.

III. The population is at least 10times as large as the sample.

(a) I only

(c) III only

(c) I, II, and III

(b) II only

(d) I and II only

65. Critical value What critical valuet*from Table Bwould you use for a 99%confidence interval for the population mean based on an SRS of size 58? If possible, use technology to find a more accurate value of t*. What advantage does the more accurate dfprovide?

Engine parts Here are measurements (in millimeters) of a critical dimension on an SRS of 16of the more than 200auto engine crankshafts produced in one day:

224.120, 224.001, 224.017,223.982,223.989,223.960,224.089,223.987,223.976,223.902,223.980,224.098,224.057,223.913,223.999

(a) Construct and interpret a 95%confidence interval for the process mean at the time these crankshafts were produced.

(b) The process mean is supposed to be μ=224but can drift away from this target during production. Does your interval from part (a) suggest that the process mean has drifted? Explain.

- Determine the sample size required to obtain a level Cconfidence interval for a population mean with a specified margin of error.

Breast-feeding mothers secrete calcium into their milk. Some of the calcium may come from their bones, so mothers may lose bone mineral. Researchers measured the percent change in bone mineral content (BMC) of the spines of 47randomly selected mothers during three months of breastfeeding. The mean change in BMC was -3.587%and the standard deviation was 2.506%.

(a) Construct and interpret a 99%confidence interval to estimate the mean percent change in BMC in the population.

(b) Based on your interval from (a), do these data give good evidence that on average nursing mothers lose bone mineral? Explain.

56. The SAT again High school students who take the SAT Math exam a second time generally score higher than on their first try. Past data suggest that the score increase has a standard deviation of about 50 points.
How large a sample of high school students would be needed to estimate the mean change in SAT score to within 2 points with 95% confidence? Show your work.

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