Question

A study on the personality characteristics of drug dealers sampled 100 convicted drug dealers and scored them each on the wanting recognition scale, which provides a quantative measure of a persons need for approval and sensitivity to social situations (higher score indicated a greater need for approval) the sample of drug dealers had a mean WR score of 56, with a standard deviation of 6. use this information to find an interval estimate of the mean WR score for wll convicted drig dealers. Use a confidence level of 95%. interpret the result.

Answer 1

Using the provided sample mean of 56 and standard deviation of 6 for the 100 convicted drug dealers, the 95% confidence interval for the mean WR score is calculated to be (54.824, 57.176), implying that we are 95% confident the true mean score for all convicted drug dealers would fall within this range.

Step-by-step explanation:

To calculate an interval estimate of the mean WR score for all convicted drug dealers with a 95% confidence level, we can use the formula for the confidence interval for the mean:

CI = \(\bar{x} \pm z\frac{\sigma}{\sqrt{n}}\)

Where \(\bar{x}\) is the sample mean, \(\sigma\) is the standard deviation, \(n\) is the sample size, and \(z\) is the z-score corresponding to the confidence level. Since the sample size (n) is 100, and given \(\bar{x} = 56\) and \(\sigma = 6\), we can find the z-score for a 95% confidence interval from the z-table, which is approximately 1.96. Thus, the confidence interval is calculated as follows:

CI = 56 \pm 1.96 * \(\frac{6}{\sqrt{100}}\)

CI = 56 \pm 1.96 * 0.6

CI = 56 \pm 1.176

Therefore, the confidence interval is (54.824, 57.176).

Interpreting this result, we are 95% confident that the population mean WR score for all convicted drug dealers falls within the interval from 54.824 to 57.176.