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Chapter 7: Problem 63

In a population of 9500 subjects, \(75 \%\) possess a certain characteristic. In a sample of 400 subjects selected from this population, \(78 \%\) possess the same characteristic. How many subjects in the population and sample, respectively, possess this characteristic?

Short Answer

Expert verified
In the population, 7125 subjects possess the characteristic, while in the sample, 312 subjects do.

Step by step solution

01

Calculate the number of subjects with the characteristic in the overall population

To find the number of subjects in the population that possess the characteristic, multiply the total population by the percentage of subjects that has this characteristic, then divide by 100. Using this method, the formula would be: \((9500 \times 75) / 100\).
02

Calculate the number of subjects with the characteristic in the sample

Similarly, to find the number of subjects in the sample that possess the characteristic, multiply the sample size by the percentage of subjects in the sample that possess the characteristic, then again divide by 100. So, the formula is: \((400 \times 78) / 100\).
03

Perform the calculations

Performing these calculations will give us the number of subjects in the population and sample that possess the characteristic.

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