Chapter 24, Problem 1E

To determine

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

Answer to Problem 1E

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. The researchers purchased samples of several different brands. A test of the null hypothesis that there is no difference in mean calorie content yields a P-value of $0.124$ . Thus, we have that a $95\%$ confidence interval for ${\mu }_{\text{Meat}}-{\mu }_{\text{Beef}}$ would include zero because a high P-value tells you that we lack evidence of a difference, so zero is a possible value for the mean, mean of meat - mean of beef.