Chapter 24, Problem 6E

(a)

To determine

To explain why you think each of the following statements is true or false.

Answer to Problem 6E

It is false.

Explanation of Solution

It is given that in June, consumer reports examined top loading and front loading washing machines testing samples of several different brands of each type. Among the machines rated good to excellent, the $98\%$ confidence interval for the difference in mean cycle time ${\mu }_{\text{Top}}-{\mu }_{\text{Front}}$ is $(-40,-22)$ . The statement is $98\%$ of top loaders are $22\text{ to 40 minutes}$ faster than front loaders. This statement is false because the confidence interval is about the mean cycle time of the washing machines, but not about the individual cycle time of the washing machines.

(b)

To determine

To explain why you think each of the following statements is true or false.

Answer to Problem 6E

It is false.

Explanation of Solution

It is given that in June, consumer reports examined top loading and front loading washing machines testing samples of several different brands of each type. Among the machines rated good to excellent, the $98\%$ confidence interval for the difference in mean cycle time ${\mu }_{\text{Top}}-{\mu }_{\text{Front}}$ is $(-40,-22)$ . The statement is if I choose the Laundromat’s top loader, there is a $98\%$ chance that my clothes will be done faster than if I had chosen the front loader. This statement is false because the confidence interval is about the mean cycle time of the washing machines, but not about the individual cycle time of the washing machines.

(c)

To determine

To explain why you think each of the following statements is true or false.

Answer to Problem 6E

It is false.

Explanation of Solution

It is given that in June, consumer reports examined top loading and front loading washing machines testing samples of several different brands of each type. Among the machines rated good to excellent, the $98\%$ confidence interval for the difference in mean cycle time ${\mu }_{\text{Top}}-{\mu }_{\text{Front}}$ is $(-40,-22)$ . The statement is if I tried more samples of both kind of washing machines, in about $98\%$ of these samples I had expect the top loaders to be an average of $22\text{ to 40 minutes}$ faster. This statement is false because other samples will almost always have other confidence intervals.

(d)

To determine

To explain why you think each of the following statements is true or false.

Answer to Problem 6E

It is true.

Explanation of Solution

It is given that in June, consumer reports examined top loading and front loading washing machines testing samples of several different brands of each type. Among the machines rated good to excellent, the $98\%$ confidence interval for the difference in mean cycle time ${\mu }_{\text{Top}}-{\mu }_{\text{Front}}$ is $(-40,-22)$ . The statement is if I tried more samples, I had expect about $98\%$ of the resulting confidence intervals to include the true difference in mean cycle time for the two types of washing machines. This statement is true because the statement contains “ $98\%$ confident” and “mean”.

(e)

To determine

To explain why you think each of the following statements is true or false.

Answer to Problem 6E

It is true.

Explanation of Solution

It is given that in June, consumer reports examined top loading and front loading washing machines testing samples of several different brands of each type. Among the machines rated good to excellent, the $98\%$ confidence interval for the difference in mean cycle time ${\mu }_{\text{Top}}-{\mu }_{\text{Front}}$ is $(-40,-22)$ . The statement is I am $98\%$ confident that top loaders wash clothes an average of $22\text{ to 40 minutes}$ faster than the front loaders. This statement is true because the statement contains “ $98\%$ confident” and “average”.