Question

The Wanting Recognition (WR) Scale provides a quantitative measure of a person's level of need for approval and sensitivity to social situations. A random sample of 100 convicted drug dealers was scoredf on the WR scale and produced a mean WR score of 39 and a standard deviation of 6. (a) Use this information, find an interval estimate of the mean WR score for all convicted drug dealers with 99% confidence level.

Answer 1

99% of the confidence level of the mean WR score for all convicted drug dealers

(37.4544, 40.5456)

Explanation:

Step(i):-

Given that the sample size 'n' = 100

Given that the mean of the sample(x⁻) = 39

Given a standard deviation of the sample (σ) = 6

Level of significance = 0.01 or 99%

Step(ii):-

99% of the confidence level of the mean WR score for all convicted drug dealers

`(x^(-) - Z_(0.01) (S.D)/(√(n) ) ,x^(-) + Z_(0.01) (S.D)/(√(n) ))`

`(39 -2.576 (6)/(√(100) ) ,39 + 2.576 (6)/(√(100) ))`

(39 - 1.5456 , 39+1.5456)

(37.4544, 40.5456)

Final answer:-

99% of the confidence level of the mean WR score for all convicted drug dealers

(37.4544, 40.5456)