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Chapter 7: Problem 62

In a population of 18,700 subjects, \(30 \%\) possess a certain characteristic. In a sample of 250 subjects selected from this population, \(25 \%\) possess the same characteristic. How many subjects in the population and sample, respectively, possess this characteristic?

Short Answer

Expert verified
In the population, 5610 subjects possess the characteristic. In the sample, there are either 62 or 63 subjects with the characteristic.

Step by step solution

01

Determine the number of subjects in the population with the characteristic

It is given that 30% of 18,700 subjects possess the characteristic. We calculate this by multiplying the total population number by the percentage of subjects with the characteristic, then dividing by 100. Hence, \(18,700 * 30 / 100 = 5610\) subjects.
02

Determine the number of subjects in the sample with the characteristic

It is given that 25% of the 250 subjects in the sample possess the characteristic. We calculate this by multiplying the sample size by the percentage of subjects in the sample with the characteristic, then dividing by 100. Hence, \(250 * 25 / 100 = 62.5\) subjects. Since the number of subjects can't be in decimal, we can assume that there is either 62 or 63 subjects with the characteristic depending on the context of the problem.

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Most popular questions from this chapter

A population has a normal distribution. A sample of size \(n\) is selected from this population. Describe the shape of the sampling distribution of the sample mean for each of the following cases. a. \(n=23\) b. \(n=450\)

The delivery times for all food orders at a fast-food restaurant during the lunch hour are normally distributed with a mean of \(7.7\) minutes and a standard deviation of \(2.1\) minutes. Find the probability that the mean delivery time for a random sample of 16 such orders at this restaurant is a. between 7 and 8 minutes b. within 1 minute of the population mean c. less than the population mean by 1 minute or more

How does the value of \(\sigma_{\hat{p}}\) change as the sample size increases? Explain. Assume \(n / N \leq .05\).

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