Chapter 8.1, Problem 22E

(a)

To determine

To Explain: the confidence interval.

Answer to Problem 22E

It is expected that about 99% of all possible samples to have a 99% confidence interval that have the correct proportion of all California adults employed in the workforce.

Explanation of Solution

The 99% confidence interval shows the proportion of all California adults employed in the workforce.

99% confidence implies that it is expected about 99% of all samples to have 99% confidence interval that has the correct population parameter.

In this case, it is expected that about 99% of all possible samples to have a 99% confidence interval that have the correct proportion of all California adults employed in the workforce.

(b)

To determine

To find: the drawbacks do these actions have.

Explanation of Solution

It can reduce the margin of error by:

• Increasing the sample size, the reason is that a large sample size would result in more details about the population and therefore the estimates are more accurate. A drawback is that it is too much time consuming and costly to gain data for a larger sample.
• Decreasing the confidence level. The reason is that there are less confident that the confidence interval has the correct population parameter and therefore the confidence interval then have less possible values for the true population parameter. A drawback is that there are less confident that the confidence interval would have the true population parameter.

(c)

To determine

To Explain: the untruthful answers may lead to bias in this survey.

Explanation of Solution

Measurement or response bias would use a method that gives different values from the true value.

If many people come in their answer, then these people could have certain common characteristics.. This then leads to consistently overestimate or consistently underestimate the true population parameters and therefore this would cause bias in our sample.

The margin of error only accounts for the possible variation and therefore is not include response bias.