Question

Age and video games Refer to Exercise 41. The study also estimated that 67% of adults aged $18–29$play video games, but only $25\%$of adults aged $65$and older play video games.

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

b. Do you think a $95\%$ confidence interval for adults aged $18–29$ would have a larger or smaller margin of error than the estimate from Exercise 41? Explain your answer.

Short answer

a. Sample sizes are unknown and sample proportions are given. It is not possible to give confidence levels.

b. It would have larger margin of error than estimate.

Step-by-step solution

Given Information

Sample size is decreasing and adults in sample is less than all individuals.

Why we do not have enough information to give confidence intervals for two age groups separately.

We should have knowledge of sample proportion and sample size to construct confidence interval. So, we do not have enough information to give confidence intervals for two age groups separately.

To check if 95% confidence interval for adults would have smaller or larger margin of error than estimate.

As number of adults are less than that in sample, we are decreasing sample size.

We have less information about population and less accurate estimates are obtained. Hence, estimate is far from true value and confidence interval has to be wider. Margin of error is larger as it is half of confidence interval.