Chapter 8.2, Problem 43E

(a)

To determine

To explain why you do not have enough information to give confidence intervals for these two age groups separately.

Explanation of Solution

Now, we do not have enough information to give confidence intervals for these two age groups separately because to construct a confidence interval assuming that the confidence level is known, we require the knowledge of the sample proportion and the sample size or the number of successes and the sample size. So, we then note that the sample sizes are unknown while the sample proportions have been given and thus it is not possible to give confidence intervals.

(b)

To determine

To explain do you think a $95\%$ confidence interval for adults aged $18-29$ would have a larger or smaller margin of error than estimate from exercise $41$ .

Answer to Problem 43E

  $95\%$ confidence interval for adults aged $18-29$ would have a larger margin of error than estimate.

Explanation of Solution

Since, in the question we are decreasing the sample size because the number of adults aged $18-29$ in the sample will be less than all individuals in the sample. If the sample size decreases then we have less information about the population and thus our estimates will be less accurate. If our estimates are less accurate then our estimate is further from the true value of the population parameter and thus the confidence interval needs to be wider. Since the margin of error is half the width of the confidence interval then the margin of error is larger.