Bird eggs A researcher wants to see if birds that build larger nests lay larger eggs. She selects two random samples of nests: one of the small nests and the other of large nests. Then she weighs one egg (chosen at random if there is more than one egg) from each nest. A $95\%$ confidence interval for the difference (Large − Small) between the mean mass (in

grams) of eggs in small and large nests is 1.6±2.0 role="math" localid="1654714720708" $\frac{305}{1526}=0.200=20.0\%1.6\pm 2.0$

a. 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? Explain your answer.

b. 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? Explain your answer.

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

role="math" localid="1654715011426" $$\begin{gathered} 1.6\pm 2.0=(1.6-2.0,1.6+2.0) \\ =(-0.4,3.6) \end{gathered}$$

Then we notice that the confidence interval contains zero, implying that the difference in mean reaction time is likely to be zero, and thus that no difference exists.

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

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

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

Then we notice that the confidence interval contains zero, implying that the difference in mean reaction time is likely to be zero, and thus that no difference exists.

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 the confidence interval for the difference contains many other plausible values.