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Explain the relationships among the sample proportion, the number of successes in the sample, and the sample size.

Short Answer

Expert verified

stands for the sample proportion.

p'=Xn is the general formula for sample proportion.

The sample proportion is obtained by dividing the sample size by the number of successes, which is the link between sample proportion, number of successes, and sample size.

Step by step solution

01

Given information

Given in the question that, we need to explain the relationships among the sample proportion, the number of successes in the sample, and the sample size.

02

Explanation

The following is the link between sample proportion, number of successes, and sample size:

The sample proportion is the fraction of the population that was taken as a sample.

p'stands for the sample proportion.

role="math" localid="1651249720477" p'=Xnis the general formula for sample proportion.

The sample proportion is obtained by dividing the sample size by the number of successes, which is the link between sample proportion, number of successes, and sample size.

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Most popular questions from this chapter

Fill in the blanks.

a. The mean of all possible sample proportions is equal to the

b. For large samples, the possible sample proportions have approximately a distribution.

c. A rule of thumb for using a normal distribution to approximate the distribution of all possible sample proportions is that both and are or greater.

Ballistic Fingerprinting. Refer to Exercise 11.110 and find and interpret a 98%confidence interval for the difference between the percentages of women and men who favor ballistic fingerprinting.

a. Determine the sample proportion.

b. Decide whether using the one-proportion z-test is appropriate.

c. If appropriate, use the one-proportion z-test to perform the specified hypothesis test.

x=3

n=100

H0:p=0.04

Ha:pโ‰ 0.04

ฮฑ=0.10

Bank Breakup. In a nationwide survey, conducted by Pulse Opinion Research, LLC for Rasmussen Reports, a sample of American adults were asked whether they favor a plan to break up the 12megabanks, which currently control about 69%of the banking industry; 50%of those sampled responded in the affirmative. According to the report, "the margin of sampling error is ยฑ3percentage points with a 95%level of confidence." Find and interpret a 95%confidence interval for the percentage of all American adults who favor a plan to break up the 12megabanks.

A poll conducted by Gallup in December 2013asked a sample of American adults whether they approved of the way President Obama was doing his job; 42%said yes, with a margin of error of plus or minus 3percentage points. During that same time period, Quinnipiac University asked the same question of a sample of American adults; 38%said yes, with a margin of error of plus or minus2 percentage points. Can the conclusions of both polls be correct? Explain your answer.

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