Chapter 11.2, Problem 24E

To determine

To find: The reasoning with reference to the mean of the entire population

Answer to Problem 24E

Yes, it is possible that the mean of the entire population is only $7.5$ hours of sleep each night.

Explanation of Solution

Given:

Sample of $200$ from a population of $2000$ .

Calculation:

The mean of the sample is $8$ hours, and the sample mean is used to estimate the parameter. So, it might be said that mean of entire population is $8$ hours. But then you need to remember that statistics only estimate the population parameter and they vary from one sample to other. That’s why there is a possibility that the mean of the entire population is only $7.5$ hours.

Conclusion:

Hence, Yes, it is possible that the mean of the entire population is only $7.5$ hours of sleep each night.