Chapter 10.2, Problem 50E

(a)

To determine

To explain does the interval provide convincing evidence of a difference in the true mean egg mass of birds with small nests and birds with large nests or not.

Answer to Problem 50E

No.

Explanation of Solution

The $95\%$ confidence interval for the difference in the mean egg mass of birds with small nests and birds with large nests:

  $\begin{array}{l}1.6\pm 2.0=(1.6-2.0,1.6+2.0)\\ =(-0.4,3.6)\end{array}$

Then we note that the confidence interval contains zero which implies that it is likely that the difference in the mean reaction time is zero and thus likely that there is no difference.

This implies that there is no convincing evidence of a difference in the true mean egg mass of birds with small nests and birds with large nests.

(b)

To determine

To explain does the interval provide convincing evidence that the true mean egg mass of birds with small nests and birds with large nests is the same or not.

Answer to Problem 50E

No.

Explanation of Solution

The $95\%$ confidence interval for the difference in the mean reaction time of athletes and non-athletes:

  $\begin{array}{l}1.6\pm 2.0=(1.6-2.0,1.6+2.0)\\ =(-0.4,3.6)\end{array}$

Then we note that the confidence interval contains zero which implies that it is likely that the difference in the mean reaction time is zero and thus likely that there is no difference.

However, there is no evidence that the true mean egg mass of birds with small nests and birds with large nests is the same because the difference of zero is one of the plausible values but there are many other plausible values in the confidence interval for the difference.