Chapter 8.1, Problem 8E

(a)

To determine

Whether the confidence interval provides convincing evidence that the true mean weight is different than 17 grams.

Answer to Problem 8E

There is no convincing evidence that the true mean weight is different than 17 grams.

Explanation of Solution

Given information:

95% confidence interval for the true mean weight:

  $\left(16.945\text{grams}-17.395\text{grams}\right)$

Note that

The confidence interval contains 17 grams.

This implies

It is likely that the true mean weight is 17 grams.

Thus,

This further implies

There is no convincing evidence that the true mean weight is different than 17 grams.

(b)

To determine

Whether the confidence interval provides convincing evidence that the true mean weight is 17 grams.

Answer to Problem 8E

Because of many other possible values for the true mean weight, there is no convincing evidence that the true mean weight is 17 grams.

Explanation of Solution

Given information:

95% confidence interval for the true mean weight:

  $\left(16.945\text{grams}-17.395\text{grams}\right)$

Note that

The confidence interval contains 17 grams.

This implies

It is likely that the true mean weight is 17 grams.

Moreover,

All weights between 16.945 grams and 17.395 grams are equally likely to be the true mean weight.

Thus,

It is not sure that the true mean weight is 17 grams.

This implies

We can’t say that there is any convincing evidence for the true mean weight is 17 grams.