1A The branch of statistics that involves using statistics computed from sample data to make statements about unknown population parameters is which of the following?

Descriptive statistics

Inferential statistics

Influential statistics

Normal statistics

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. Based on this, using both the appropriate symbol and in words, state the one parameter of interest.

1B The parameter of interest isthedifferencein 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.

The parameter of interest is₁-_2,thedifferencein 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.

The parameter of interest is ₂, the mean sale price of all white cars sold at used car auctions.

The parameter of interest is ₁the mean sale price of all black cars sold at used car auctions

Used Car Auctions

Suppose population 1 is all blue cars sold at used car auctions, and the mean sale price of all such blue cars is $24,579 with a standard deviation of $3,691. Additionally suppose population 2 is all red cars sold at used car auctions, and the mean sale price of all such red cars is $21,948 with a standard deviation of $4,028. If a simple random sample of 47 blue cars sold at used car auctions is selected and = the mean sale price of the 47 blue cars in the sample is determined, and if an independent simple random sample of 59 red cars sold at used car auctions is selected and the mean sale price of the 59 red cars in the sample is determined, if appropriate describe completely the sampling distribution of .

1C What is the mean of the sampling distribution?

12

2631

4631

337

2A If both populations are known to be normal, what size samples are required to complete the inferences?

Sample sizes must both be 40 or greater

Sample sizes must both be 15 or greater

Sample sizes do not matter

Used Car Auctions

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 parameterthe 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 $18,225 and a standard deviation of $6,395. If appropriate, use this information tocalculate and interpreta 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

2B 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?

Neither the margin of error nor the width would be affected.

Both the margin of error and the width would decrease.

The margin of error would decrease and the width would increase.

The margin of error would increase and the width would decrease.

Both the margin of error and the width would increase.

2C Are the populations normal or the sample sizes large enough for the central limit theorem to apply?

Yes because the populations are normal

Yes

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

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.

The two most recent tests in STAT 210 have been tests 5 and 6. Suppose population 1 consists of all students who took both tests and who picked up test 5 from their instructor prior to test 6, while population 2 consists of all students who took both tests but did not pick up test 5 from their instructor prior to test 6. It is conjectured that the mean score on test 6 for all students who picked up test 5 is greater than the mean score on test 6 for students who did not pick up test 5. State the appropriate null and alternative hypotheses that should be tested.

H₀:₁=₂H_a:₁>₂

H₀:₁=₂H_a:_1<2

H₀: X-bar₁= X-bar₂H_a: X-bar₁>X-bar₂

H₀:₁=₂H_a:₁₂