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 42.7%. Suppose these results are based on a random sample of 1,900 people under 20 years old who were eligible to have a driver's license in year A and an 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-- V than the margin of error in part (b). This is because the sample proportion of eligible people under 20 years old whad a driver's license in year B is 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--- ✓ interval estimate in part (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.)Solution:(a)For year A, 62.9% of eligible people under 20 years old had a driver's license.

Sample size, n = 1,900 Using the given formula,Margin of error (E) = Zα/2 × (σ/√n)Zα/2 = the z-value for the level of confidence. At 95% confidence, α = 0.05 and therefore the z-value is 1.96σ = the standard deviation for a population proportion. For a proportion p, σ = √(p (1-p)/n)σ = √[(62.9/100) (1-0.629)/1900]σ = 0.0147 Margin of error (E) = 1.96 × (0.0147/√1900)E = 0.0050 The margin of error for the number of eligible people under 20 years old who had a driver's license in year A is 0.0050.Applying this margin of error to the percentage of 62.9%, the 95% confidence interval estimate is [0.6249, 0.6349].(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.)Solution:(b)For year B, 42.7% of eligible people under 20 years old had a driver's license. Sample size, n = 1,900Using the given formula,Margin of error (E) = Zα/2 × (σ/√n)Zα/2 = the z-value for the level of confidence.

At 95% confidence, α = 0.05 and therefore the z-value is 1.96σ = the standard deviation for a population proportion. For a proportion p, σ = √(p (1-p)/n)σ = √[(42.7/100) (1-0.427)/1900]σ = 0.0151Margin of error (E) = 1.96 × (0.0151/√1900)E = 0.0051The margin of error for the number of eligible people under 20 years old who had a driver's license in year B is 0.0051.Applying this margin of error to the percentage of 42.7%, the 95% confidence interval estimate is [0.4220, 0.4334].(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-- V 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 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---  interval estimate in part (b).The margin of error in part (a) is less 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 less than the sample proportion of eligible people under 20 years old who had a driver's license in year A. This leads to a wider interval estimate in part (b).

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