Chapter 24, Problem 3E

(a)

To determine

To explain what does “the endpoints of this confidence interval are negative” indicate.

Explanation of Solution

It is given that in July, consumer reports examined the calorie content of two kinds of hot dogs: meat and all beef also listed the sodium content for the various hot dogs tested. The researchers purchased samples of several different brands. The resulting $90\%$ confidence interval for ${\mu }_{\text{Meat}}-{\mu }_{\text{Beef}}$ is $(-6.5,-1.4)$ . Thus, the endpoints of this confidence interval are negative indicates that the difference ${\mu }_{\text{Meat}}-{\mu }_{\text{Beef}}$ is negative and thus that mean fat content of beef hot dogs is higher than the mean fat content of meat hot dogs.

(b)

To determine

To explain what does the fact that the confidence interval does not contain zero indicate.

Explanation of Solution

It is given that in July, consumer reports examined the calorie content of two kinds of hot dogs: meat and all beef also listed the sodium content for the various hot dogs tested. The researchers purchased samples of several different brands. The resulting $90\%$ confidence interval for ${\mu }_{\text{Meat}}-{\mu }_{\text{Beef}}$ is $(-6.5,-1.4)$ . Thus, the fact that the confidence interval does not contain zero indicate that since the confidence interval does not contain zero, this indicate that the difference ${\mu }_{\text{Meat}}-{\mu }_{\text{Beef}}$ is nonzero and thus the mean fat content of beef hot dogs is significantly different from the mean fat content of meat hot dogs.

(c)

To determine

To explain what does the corresponding alpha level.

Answer to Problem 3E

The corresponding alpha levelis $0.10$ .

Explanation of Solution

It is given that in July, consumer reports examined the calorie content of two kinds of hot dogs: meat and all beef also listed the sodium content for the various hot dogs tested. The researchers purchased samples of several different brands. The resulting $90\%$ confidence interval for ${\mu }_{\text{Meat}}-{\mu }_{\text{Beef}}$ is $(-6.5,-1.4)$ . It is given that if we use this confidence interval to test the hypothesis that ${\mu }_{\text{Meat}}-{\mu }_{\text{Beef}}=0$ . Thus, as given the confidence level $90\%$ , we have the corresponding alpha level of the two-sided test is one decreased by the confidence level as:

  $\begin{array}{l}\alpha =1-90\%\\ =1-0.90\\ =0.10\end{array}$