Chapter 24, Problem 2E

To determine

To explain would a $95\%$ confidence interval for ${\mu }_{\text{Meat}}-{\mu }_{\text{Beef}}$ include zero.

Answer to Problem 2E

Yes, it will include zero.

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. A test of the null hypothesis that the beef hot dogs and the meat hot dogs do not differ in the mean amounts of sodium yields a P-value of $0.11$ . Thus, we have that a $95\%$ confidence interval for ${\mu }_{\text{Meat}}-{\mu }_{\text{Beef}}$ would include zero because the P-value of $0.11$ is larger than $0.05$ , thus we would fail to reject the null hypothesis and the confidence interval then contains zero because they do not appear to differ in mean.