Chapter 7.1, Problem 16E

To determine

To find: the convincing evidence that the average height of all 16 year old females at this school is greater than 64 inches, explain.

Answer to Problem 16E

Yes

Explanation of Solution

Every dot in the given dot plot represents a sample $\overline{x}$ for a simple random sample with twenty 16-year-old females, while the sample mean is representing the mean height of the individuals in the sample.

There are no dots above $65.8$ inches and there are also no dots to the right of $65.8$ inches in the given dot plot. This then is indicating that it is very unlikely to occur a sample mean of at least $65.8$ inches, when the population mean is actually $64$ inches. Therefore it is surprising to get a sample mean of $65.8$ or larger.

This then also means that there is no convincing evidence that the average height of all 16-year-old females at this school is greater than 64 inches.