Chapter 7.1, Problem 13E

(a)

To determine

The description of approximate sampling distribution.

Answer to Problem 13E

The sampling distribution is right-skewed.

Explanation of Solution

Given information:

Thermostat set to prevent the pipes from freezing $=50°\text{F}$

Standard deviation, $\sigma =3°\text{F}$

Number of readings during 24-hour period for SRS, $n=10$

Mean, $\mu =50°\text{F}$

The dotplot:

  

It is seen that the given dotplot has the highest columns of dots to the left and a tail to the right. This means that the sampling distribution is right-skewed.

In the dotplot, it is seen that the sampling distribution is centered at about $9{\left(°\text{F}\right)}^2$ as the center of the right-skewed distribution is slightly placed to the right of the highest points of the graph.

The range of values is roughly from $2{\left(°\text{F}\right)}^2$ to $27{\left(°\text{F}\right)}^2$ .

Hence, the sampling distribution is right-skewed.

(b)

To determine

The conclusion about the thermostat manufacturer’s claim.

Answer to Problem 13E

The thermostat manufacturer’s claim is false.

Explanation of Solution

Given information:

Thermostat set to prevent the pipes from freezing $=50°\text{F}$

Standard deviation, $\sigma =3°\text{F}$

Number of readings during 24-hour period for SRS, $n=10$

Mean, $\mu =50°\text{F}$

Variance from an actual sample, $s_x{}^2=25$

The dotplot:

  

In the given dotplot it is seen that no dots are above 25. There is only one dot to the right; which means a sample variance of 25 cannot be obtained.

Hence, it can be concluded that the thermostat manufacturer’s claim is false.