Chapter 24, Problem 5E

(a)

To determine

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

Answer to Problem 5E

It is false.

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 $(-6.5,-1.4)$ . The statement is if I eat a meat dog instead of a beef dog there is a $90\%$ chance I will consume less fat. This statement is false because the confidence interval is about the mean fat content of the hotdogs, but not about the individual fat content of hotdogs.

(b)

To determine

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

Answer to Problem 5E

It is false.

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 $(-6.5,-1.4)$ . The statement is $90\%$ of meat dogs have between $1.4\text{ and 6}\text{.5 grams}$ less fat than a beef hot dog. This statement is false because the confidence interval is about the mean fat content of the hotdogs, but not about the individual fat content of hotdogs.

(c)

To determine

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

Answer to Problem 5E

It is true.

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 $(-6.5,-1.4)$ . The statement is I am $90\%$ confident that meat hot dogs average $1.4-\text{6}\text{.5 grams}$ less fat than the beef hot dogs. This statement is true because the statement contains “ $90\%$ confident” and “average”.

(d)

To determine

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

Answer to Problem 5E

It is false.

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 $(-6.5,-1.4)$ . The statement is if I were to get more samples of both kinds of hot dogs $90\%$ of the time the meat hot dogs would average $1.4-\text{6}\text{.5 grams}$ less fat than the beef hot dogs. This statement is false because other samples will almost always have other confidence intervals.

(e)

To determine

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

Answer to Problem 5E

It is true.

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 $(-6.5,-1.4)$ . The statement is if I tested many samples I had expect about $90\%$ of the resulting confidence intervals to include the true difference in mean fat content between the two kinds of hot dogs. This statement is true because the statement contains “ $90\%$ confident” and “mean”.