Question

CENGAGE | MINDTAP Q Search this course Chapter 8 Assignment Check My Work 8. O 9. d eBook 10. O 11. O Fewer young people are driving. In 1983, 87% of 19-year-olds had a driver's license. Twenty-five years later that percentage had dropped to 75% (University of Michigan Transportation Research Institute website, April 7, 2012). Suppose these results are based on a random sample of 1200 19-year-olds in 1983 and again in 2008. a. At 95% confidence, what is the margin of error and the interval estimate of the number of 19-year-old drivers in 1983? Round your intermediate answers to four decimal places. Margin of error = (four decimal places) Interval estimate (to four decimal places) = to b. At 95% confidence, what is the margin of error and the interval estimate of the number of 19-year-old drivers in 2008? Round your answers to four decimal places. Margin of error = Interval estimate = c. Is the margin of error the same in parts (a) and (b)? - Select your answer - Why, or why not? The input in the box below will not be graded, but may be reviewed and considered by your instructor. Check My Work 0= Icon Key

Answer 1

(a)

Sample size = n = 1200 Sample proportion = p = 0.87 Stanadard Error = 2 = sqrt(0.87*(1-0.87)/1200) = 0.0097 ✓n Confidence Level = 95 Significance Level = a = (100-95)% = 0.05 Critical value = z* = 1.96 [Using Excel =ABS(NORMINV(0.05/2,0,1))] Margin of Error = z*(standard error )= 1.96*0.0097 = 0.01903 Lower Limit =- Margin of Error = 0.87 -0.01903 = 0.851 Upper Limit =ộ + Margin of Error = 0.87 + 0.01903 = 0.889 Ans:(0.851, 0.889)

(b)

Sample size = n = 1200 Sample proportion = p = 0.75 Stanadard Error = P = sqrt(0.75*(1-0.75)/1200) = 0.0125 V n Confidence Level = 95 Significance Level = a = (100-95)% = 0.05 Critical value = z* = 1.96 [Using Excel =ABS(NORMINV(0.05/2,0,1))] Margin of Error = z* (standard error )= 1.96*0.0125 = 0.0245 Lower Limit =- Margin of Error = 0.75 -0.0245 = 0.7255 Upper Limit =p + Margin of Error = 0.75 +0.0245 = 0.7745 Ans:(0.7255, 0.7745 )

(c) NO

As the sample proportion decreases, margin of error increases.