Round intermediate and final answers to at least three decimal places.

Question

Manual Transmission Automobiles In a recent year, 6%

 of cars sold had a manual transmission. A random sample of college students who owned cars revealed the following: out of 130

 cars, 20

 had manual transmissions. Estimate the proportion of college students who drive cars with manual transmissions with 95%

 confidence. Round intermediate and final answers to at least three decimal places.

Answer 1

Use the formula for a (1-α)100% confidence interval for π, the population proportion of college students who drive a manual,.

They want a 95% confidence interval for the proportion of college students who drive a manual. The Z-score corresponding to a 95% confidence interval is Z = 1.96. A random sample of n = 130 college students reveals that 20 drive a manual. So, x = 20 and n = 130. The point estimate for the population proportion, π, is phat = x/n = 20/130 = 0.15385.

Use the formula phat ± Z(1-α/2)*sqrt((phat)(1-phat)/n) =20/130±1.96*sqrt((20/130)(1-20/130)/130) =

.15385 ± 1.96*.03164 =

.15385 ± .06202 = 0.09182 to 0.21587

We can be 95% confident that the true proportion of college students who drive a manual is between 0.09182 and 0.21587.

Notice that since this interval falls entirely above the stated general population proportion of 0.06, it would appear that the proportion of college students who drive a manual is higher than the population proportion.