A study on the personality characteristics of drug dealers sampled 100 convicted drug dealers and scored them each on the Wanting Recognition? (WR) Scale, which provides a quantitative measure of a? person's need for approval and sensitivity to social situations.? (Higher scores indicate a greater need for? approval.) The sample of drug dealers had a mean WR score of 52?, with a standard deviation of 4. Use this information to find an interval estimate of the mean WR score for all convicted drug dealers. Use a confidence level of 90?%. Interpret the result.

a.) The 90?% confidence interval for mean WR score indicates that the true mean WR score for convicted drug dealers is between _ and _ with 90% confidence.
b.) The 90?% confidence interval for mean WR score indicates that 90?% of convicted drug dealers have a WR score between _ and _ .
c.) The 90?% confidence interval for mean WR score indicates that the true mean WR score for all drug dealers is between _ and _ with 90% confidence.
d.) The 90?% confidence interval for mean WR score indicates that 90?% of all drug dealers have a WR score between _ and _ .

Since the standard deviation is not known , we will be using the Student's t-distribution. So, assuming the Wanting Recognition scores are approximately Normally distributed, The 90% confidence interval is given by the interval

[tex]\large [\bar x-t^*\frac{s}{\sqrt n}, \bar x+t^*\frac{s}{\sqrt n}][/tex]

where

[tex]\large \bar x[/tex] is the sample mean

s is the sample standard deviation

n is the sample size

[tex]\large t^*[/tex] is the value such that the area under the Student's t-distribution with 99 degrees of freedom (sample size -1) between [tex]\large [t^*, +t^*][/tex] is 90% or 0.9

Either by using a table or the computer, we find

[tex]\large t^*= 1.29[/tex]

and our 90% confidence interval is

\bf [52-1.29*\frac{4}{\sqrt{100}}, 52+1.29*\frac{4}{\sqrt{100}}]=[51.484,52.516]

This 90% confidence interval for mean WR score indicates that 90% of convicted drug dealers have a WR score between 51.484 and 52.516

joaobezerra joaobezerra · Answer 2 · 2022-03-24T12:14:14+01:00

Using the interpretation of the confidence interval, it is found that the correct option is given by:

c.) The 90% confidence interval for mean WR score indicates that the true mean WR score for all drug dealers is between 51.34 and 52.66 with 90% confidence.

What is the interpretation of a x% confidence interval?

It means that we are x% confident that the population parameter(mean/proportion/standard deviation) is between a and b.

In this question, we have that considering a 90% confidence interval, with a critical value of z = 1.645, the interval is given by:

[tex]52 - 1.645\frac{4}{\sqrt{100}} = 51.34[/tex]

[tex]52 + 1.645\frac{4}{\sqrt{100}} = 52.66[/tex]

Hence the correct option is given by:

c.) The 90% confidence interval for mean WR score indicates that the true mean WR score for all drug dealers is between 51.34 and 52.66 with 90% confidence.

More can be learned about confidence intervals at https://brainly.com/question/25890103