Used car auctions give car dealers an opportunity to increase their used car inventory by purchasing cars used as rental cars, assigned to company executives, and other similar activities. Suppose population 1 is all black cars sold at used car auctions, and population 2 is all white cars sold at used car auctions. Of interest is to estimate the difference in the mean sale price of all black cars sold at used car auctions and the mean sale price of all white cars sold at used car auctions To estimate the parameter the following was done. A group of 12 black sports cars being sold at used car auctions was selected. The distribution of the costs of these cars is heavily skewed to the right, with a mean of $125,310 and a standard deviation of $42,255. A group of 24 white compact cars being sold at used car auctions was selected. The distribution of the costs of these cars is fairly symmetric, with a mean of $18,2 and a standard deviation of $42,255. A group of 24 white compact cars being sold at used car auctions was selected. The distribution of the costs of these cars is fairly symmetric, with a mean of $18,225 and a standard deviation of $6,395. If appropriate, use this information to calculate and interpret a 90% confidence interval for the difference in the mean sale price of all black cars sold at used car auctions and the mean sale price of all white cars sold at used car auctions .
1. Do we have simple random samples?
A. Yes.
B. No.
2. Are the populations normal or the sample sizes large enough for the central limit theorem to apply?
A. No, because the first population was heavily skewed, but the sample size of 12 is too small for the CLT to apply (the sample size must be greater than or equal to 40 if the population is heavily skewed.) Central limit theorem does not apply.
B. Yes, because although the populations are not known to be normal, the sample sizes of 12 and 24 are both large enough for the central limit theorem to apply.
C. Yes because the populations are normal.
D. Yes.
3. If the confidence level were decreased from 95% to 90%, what impact would this have on the margin of error and width of the confidence interval?
A. Both the margin of error and the width would increase.
B. The margin of error would decrease and the width would increase.
C. Neither the margin of error nor the width would be affected.
D. Both the margin of error and the width would decrease.
E. The margin of error would increase and the width would decrease.