91Ó°ÊÓ

We need to find the evidence for an average height of females.

We know that

Sample mean is,$\stackrel{¯}{x}=64.7$

Therefore, The sample mean of $64.7$inches, which is greater than $64$inches, is proof that the "average height of all $16$-year-old females at this school is greater than $64$inches, on average."

We need to find the explanations for the evidence described in part (a).

Because the population mean height is $64$inches and we got a sample with a sample mean of $64.7$inches by chance, it's feasible that the sample mean is more than $64$inches.

However, it's also feasible that the sample mean is bigger than $64$inches because the population's average height is higher.

We need to find the representation of value $62.5$.

Each dot in the dotplot indicates a sample mean $x$for a simple random sample (SRS) of twenty $16$-year-old females, where the sample mean is the sample's average height.

The $62.5$-inch dot indicates a simple random sample of twenty $16$-year-old females with a sample mean height of $62.5$inches.

We need to find out whether the value sample mean is surprising or not.

In the above dotplot, there are $11$ dots above $64.7$ inches and several dots to the right of $64.7$ inches. When the population mean is $64$ inches, this means that a sample mean of at least $64.7$ inches is very likely to be obtained. As a result, a sample mean of $64.7$ or higher is not uncommon.

We need to find the convincing evidence for the part (d).

From part (d)

We know that

It is not surprising to get the sample mean greater than or equal to the given sample mean.

Which means that there is no persuasive evidence that all $16$-year-old females at this school are taller than $64$inches.

Therefore, there is no evidence.