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Chapter 11: Q.11.8 (page 459)

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

x=8,n=40,95%level

We have given the number of successes and the sample size for a simple random sample from a population. In each case, do the following tasks.

a. Determine the sample proportion.

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

c. If appropriate, use the one-proportion z-interval procedure to find the confidence interval at the specified confidence level.

d. If appropriate, find the margin of error for the estimate of pand express the confidence interval in terms of the sample proportion and the margin of error

11.97 Sunscreen Use. Industry Research polled teenagers on sunscreen use. The survey revealed that 46% of teenage girls and 30% of teenage boys regularly use sunscreen before going out in the sun.
a. Identify the specified attribute.
b. Identify the two populations.
c. Are the proportions 0.46(46%) and 0.30(30%) sample proportions or population proportions? Explain your answer.

Is a population proportion a parameter or a statistic? What about a sample proportion? Explain your answers.

Literate Adults. Suppose that you have been hired to estimate the percentage of adults in your state who are literate. You take a random sample of 100adults and find that 96are literate. You then obtain a 95%confidence interval of

0.96卤1.96路(0.96)(0.04)/100

or 0.922to 0.998. From it you conclude that you can be 95%confident that the percentage of all adults in your state who are literate is somewhere between 92.2%and 99.8%. Is anything wrong with this reasoning?

In this Exercise, we have given the number of successes and the sample size for a simple random sample from a population. In each case, do the following tasks.

a. Determine the sample proportion.

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

c. If appropriate, use the one-proportion z-interval procedure to find the confidence interval at the specified confidence level.

d. If appropriate, find the margin of error for the estimate of pand express the confidence interval in terms of the sample proportion and the margin of error:

x=10,n=40,90%level
See all solutions

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