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Chapter 7: Problem 61

In a population of 5000 subjects, 600 possess a certain characteristic. In a sample of 120 subjects selected from this population, 18 possess the same characteristic. What are the values of the population and sample proportions?

Short Answer

Expert verified
The population proportion is 0.12 and the sample proportion is 0.15.

Step by step solution

01

Calculate Population Proportion

To calculate the population proportion, divide the number of subjects in the population with the characteristic by the total number of subjects in the population. So the population proportion (P) is \( P = \frac{600}{5000} \).
02

Calculate Sample Proportion

To calculate the sample proportion, divide the number of subjects in the sample with the characteristic by the total number of subjects in the sample. So the sample proportion (p) is \( p = \frac{18}{120} \).
03

Calculate Values

Now we'll actually compute these values. Doing the divisions, we find that \( P = 0.12 \) and \( p = 0.15 \).

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Most popular questions from this chapter

A certain elevator has a maximum legal carrying capacity of 6000 pounds. Suppose that the population of all people who ride this elevator have a mean weight of 160 pounds with a standard deviation of 25 pounds. If 35 of these people board the elevator, what is the probability that their combined weight will exceed 6000 pounds? Assume that the 35 people constitute a random sample from the population.

If all possible samples of the same (large) size are selected from a population, what percentage of all the sample means will be within \(1.5\) standard deviations \(\left(\sigma_{\bar{x}}\right)\) of the population mean?

For a population, \(N=2800\) and \(p=.29 .\) A random sample of 80 elements selected from this population gave \(\hat{p}=.33\). Find the sampling error.

Refer to Exercise \(7.100\). Assume that \(73 \%\) of adults age 18 years and older are in favor of raising taxes on those with annual incomes of \(\$ 1\) million or more to help cut the federal deficit. A random sample of 900 American adults age 18 years and older is selected. a. Find the probability that the sample proportion is i. less than \(.76\) ii. between \(.70\) and \(.75\) b. What is the probability that the sample proportion is within \(.025\) of the population proportion? c. What is the probability that the sample proportion is greater than the population proportion by 03 or more?

According to an estimate, the average age at first marriage for men in the United States was \(28.2\) years in 2010 (Time, March 21, 2011). Suppose that currently the mean age for all U.S. men at the time of first marriage is \(28.2\) years with a standard deviation of 6 years and that this distribution is strongly skewed to the right. Let \(\bar{x}\) be the average age at the time of first marriage for 25 randomly selected U.S men. Find the mean and the standard deviation of the sampling distribution of \(\bar{x}\). What if the sample size is \(100 ?\) How do the shapes of the sampling distributions differ for the two sample sizes?
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