Chapter 7.1, Problem 14E

(a)

To determine

The description about the approximate sampling distribution.

Answer to Problem 14E

The approximate sampling distribution is roughly symmetric.

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 in the middle. This means the sample distribution is roughly symmetric.

It is known that the center of a symmetric distribution is roughly stays at the highest point of the graph. So, the sampling distribution is centered at about $45°\text{F}$ .

This gives that the range of values is from roughly $39°\text{F}$ to $50°\text{F}$ .

Hence, the approximate sampling distribution is roughly symmetric.

(b)

To determine

The conclusion about the thermostat manufacturer’s claim.

Answer to Problem 14E

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, $\mu =50°\text{F}$

Minimum of the actual sample = $40°\text{F}$

The dotplot:

  

In the given dotplot it is seen that no dots are above 40. There is only one dot to the left; which means a sample minimum of 40 cannot be obtained.

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