Chapter 8.1, Problem 20E

(a)

To determine

To Explain: that if the confidence levels were decreased to 90 percent, happen to the length of the interval.

Answer to Problem 20E

Decreases

Explanation of Solution

If the decrease the confidence level from 95% to 90%, then there are less confident that the confidence interval would have the correct population parameter and therefore the confidence interval requires having less possible values for the correct population parameter.

This then means that the confidence interval requires being narrower and therefore the length of the interval deceases.

(b)

To determine

To Explain: that 95 percent confidence interval on the basis of triple the sample size comparing to the original 95 percent interval.

Answer to Problem 20E

Confidence interval on the basis of triple the sample size is narrower than the original confidence interval.

Explanation of Solution

Tripling the sample size and therefore the sample size increases

If the sample size increases, then have more details about the population and therefore our estimates would be more accurate.

If estimates are more accurate, then estimate is closer to the correct value of the population parameter and therefore the confidence interval requires being narrower.

(c)

To determine

To find: the other potential sources of error can affect the accuracy of the 95 percent confidence interval.

Explanation of Solution

The margin of error only includes possible variation and therefore does not account for the errors made during the collection of the sample data.

Other possible types of bias are:

Selection or under coverage bias would exclude part of the population.

Measurement or response bias would use a procedure that gives different values from the correct value.

Non response bias is the results of not contain data for everybody in the sample.