Chapter 7.1, Problem 10E

(a)

To determine

Whether the distribution is the sampling distribution of $\overline{x}$ or not.

Answer to Problem 10E

The distribution is not the sampling distribution of $\overline{x}$ .

Explanation of Solution

Given information:

Mean, $\mu =64$ inches

Standard deviation, $\sigma =2.5$ inches

Number of 16-year old females = 300

Number of 16-year old females for SRS = 20

The population distribution = $N\left(64,2.5\right)$

The dotplot:

  

Here, the sampling distribution should contain all possible samples of size 20.

But in the given distribution, the dotplot contains 250 results of random samples whose size is 20.

Hence, the distribution is not the sampling distribution of $\overline{x}$ .

(b)

To determine

The description of the distribution. Also, find whether there are any obvious outliers or not.

Answer to Problem 10E

The histogram has 2 outliers.

Explanation of Solution

Given information:

Mean, $\mu =64$ inches

Standard deviation, $\sigma =2.5$ inches

Number of 16-year old females = 300

Number of 16-year old females for SRS = 20

The population distribution = $N\left(64,2.5\right)$

The dotplot:

  

The highest peak is roughly in the middle of the histogram; so the shape of the histogram is roughly unimodal and symmetric. Also, the highest peak of the histogram is at about 64.0. This means, the distribution is centered at 64.0. It is also seen that the values of data vary from 62.5 to 65.7 in the histogram.

Observe that there is one outlier on each side of the dotplot. This means the histogram has total 2 outliers and they are 62.5 and 65.7.

Hence, the histogram has 2 outliers.

(c)

To determine

The conclusion about the population mean height $\mu$ for the 16-year-old females at the school.

Answer to Problem 10E

The given claim is true.

Explanation of Solution

Given information:

Mean, $\mu =64$ inches

Standard deviation, $\sigma =2.5$ inches

Number of 16-year old females = 300

Number of 16-year old females for SRS = 20

The population distribution = $N\left(64,2.5\right)$

The dotplot:

  

The given population distribution is $N\left(64,2.5\right)$ .

It is seen n the dotplot that above 64.7 there are a lot of dots and a lot dots to its right side.

This means that if the population distribution is $N\left(64,2.5\right)$ , then it will be likely to obtain a sample mean of 64.7.

Hence, it is concluded that the claim is true.