Chapter 7.1, Problem 14E

(a)

To determine

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

Answer to Problem 14E

Sample mean is 64.7 which is greater than 64 inches

Explanation of Solution

Given:

  $\overline{x}=\text{64}\text{.7}$

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

(b)

To determine

To Explain: the two explanations for the evidence described in part (a).

Explanation of Solution

Given:

  $\overline{x}=\text{64}\text{.7}$

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

It is possible that the sample mean is greater than 64 inches, the reason behind is that the population mean height is actually 64 inches and it is obtained a sample with sample mean of 64.7 inches by chance.

Although, it is also possible that the sample mean is greater than 64 inches, the reason behind is that the population mean height is actually higher than 64 inches.

(c)

To determine

To Explain: this value represents.

Explanation of Solution

Given:

  

By seeing the dot plot, it is observed that dot in the given dot plot represents a sample $\overline{x}$ for a simple random sample with 20 16-year-old females, where the sample mean represent the mean height of the individuals in the sample.

The dot at 62.5 then represents one simple random sample of 20 16-years-old females in which the sample mean height is 62.5 inches.

(d)

To determine

To Explain: that would it be surprising to get a sample mean or larger in an SRS of size 20 when mean 64 inched and standard deviation is 2.5 inches.

Explanation of Solution

By seeing the do plot, it is observed that every dot in the given dot plot represents a sample $\overline{x}$ for a simple random sample with 20 16-year-old females, where the sample mean represent the mean height of the individuals in the sample.

There are 11 dots above 64.7 inches and there are also many dots to the right of 64.7 inches in the given dot plot. This then indicates that it is very likely to obtain a sample mean of at least 64.7 inches, when the population mean is actually 64 inches. Therefore it is not surprising to get a sample mean of 64.7 or larger.

(e)

To determine

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

Explanation of Solution

By seeing the dot plot it is observed that each dot in the given dot plot represents a sample $\overline{x}$ for a simple random sample with 20 16-year-old females, where the sample mean represent the mean height of the individuals in the sample.

There are 11 dots above 64.7 inches and there are also many dots to the right of 64.7 inches in the given dot plot. This then indicates that it is very likely to obtain a sample mean of at least 64.7 inches, when the population mean is actually 64 inches. Therefore it is not surprising to get a sample mean of 64.7 or larger.

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