Question

Fewer young people are driving. In year A, 62.9% of people under 20 years old who were eligible had a driver's license. Twenty years later in year B that percentage had dropped to 46.7%. Suppose these results are based on a random sample of 1,700 people under 20 years old who were eligible to have a driver's license in year A and again in year B.

(a)

At 95% confidence, what is the margin of error of the number of eligible people under 20 years old who had a driver's license in year A? (Round your answer to four decimal places.)

At 95% confidence, what is the interval estimate of the number of eligible people under 20 years old who had a driver's license in year A? (Round your answers to four decimal places.)

to

(b)

At 95% confidence, what is the margin of error of the number of eligible people under 20 years old who had a driver's license in year B? (Round your answer to four decimal places.)

At 95% confidence, what is the interval estimate of the number of eligible people under 20 years old who had a driver's license in year B? (Round your answers to four decimal places.)

to

(c)

Is the margin of error the same in parts (a) and (b)? Why or why not?

The margin of error in part (a) is ---Select--- smaller larger than the margin of error in part (b). This is because the sample proportion of eligible people under 20 years old who had a driver's license in year B is ---Select--- closer to 0 closer to 0.5 closer to 1 than the sample proportion of eligible people under 20 years old who had a driver's license in year A. This leads to a ---Select--- smaller larger interval estimate in part (b).

Answer 1

To calculate the margin of error and interval estimate for the number of eligible people under 20 years old who had a driver's license in year A and year B, we use the formula Margin of Error = z * sqrt((p * (1-p))/n) and Interval Estimate = p +/- Margin of Error. The margin of error is larger in part (b) because the sample proportion in year B is further away from 0.5 than in year A.

Step-by-step explanation:

Step-by-step explanation:

To calculate the margin of error and interval estimate for the number of eligible people under 20 years old who had a driver's license in year A, we can use the formula:

Margin of Error = z * sqrt((p * (1-p))/n)

Interval Estimate = p +/- Margin of Error

where z is the z-score for the desired confidence level (in this case, 95% confidence), p is the sample proportion, and n is the sample size.

For part (a), the sample proportion in year A is 62.9% or 0.629. Plugging this value into the formula, we can calculate the margin of error and interval estimate.

For part (b), the sample proportion in year B is 46.7% or 0.467. Plugging this value into the same formula, we can calculate the margin of error and interval estimate.

The margin of error is different in parts (a) and (b) because the sample proportion in year B is further away from 0.5 than in year A. This leads to a larger interval estimate in part (b).