Question

You may need to use the appropriate appendix table or technology to answer this 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 44.7%. Suppose these results are based on a random sample of 1,300 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?

Answer 1

The margin of error of the number of eligible people under 20 years old who had a driver's license in year A is approximately 0.023.

Step-by-step explanation:

To find the margin of error of the number of eligible people under 20 years old who had a driver's license in year A, we need to calculate the standard error. The formula for the standard error is:

Standard Error = square root(p(1-p)/n)

Where p is the proportion of people under 20 years old who had a driver's license in year A and n is the sample size. In this case, p = 0.629 and n = 1300. Plugging these values into the formula, we get:

Standard Error = square root(0.629*(1-0.629)/1300) ≈ 0.012

Finally, to find the margin of error, we multiply the standard error by the critical value associated with a 95% confidence level. For a 95% confidence level, the critical value is approximately 1.96. Therefore, the margin of error is:

Margin of Error = 1.96 * Standard Error ≈ 1.96 * 0.012 ≈ 0.023