Question

In an investigation of the personality characteristics of drug dealers of a certain? region, convicted drug dealers were scored on a scale that provides a quantitative measure of a? person's level of need for approval and sensitivity to social situations.? (Higher scores indicate a greater need for? approval.) Based on the study? results, it can be assumed that the scale scores for the population of convicted drug dealers of the region has a mean of 36 and a standard deviation of 7 . Suppose that in a sample of 85 people from the? region, the mean scale score is x overbar equals37 . Is this sample likely to have been selected from the population of convicted drug dealers of the? region? Explain. Consider an event with a probability less than 0.05 unlikely. Select the correct choice below and fill in the answer box within your choice. ?(Round to four decimal places as? needed.)

A. ?No, because the probability that a randomly selected sample of convicted drug dealers of the region has a sample mean of 37 or less is nothing which is greater than 0.05.

B. Yes ?, because the probability that a randomly selected sample of convicted drug dealers of the region has a sample mean of 37 or greater is nothing which is greater than 0.05.

C. No ?, because the probability that a randomly selected sample of convicted drug dealers of the region has a sample mean of 37 or greater is nothing which is less than 0.05.

Answer 1

For determining whether the sample is likely to have been selected from the population of convicted drug dealers we construct a 95% (Given: ? = 0.05) confidence interval for the mean = 36, Standard deviation =7. Sample size n = 85.

So upper limit of confidence interval UL: , z for 95% confidence interval = 1.96.

U.L = = 37.49.

L.L = = 34.51

So the 95% confidence interval is: (34.51,37.49)

In our sample, the mean score comes out to be 37 which is well within our confidence interval range.

So Ans.) B