MATH SOLVE

3 months ago

Q:
# 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 ___ .

Accepted Solution

A:

Answer:The 90% confidence interval for mean WR score indicates that 90% of convicted drug dealers have a WR score between 51.484 and 52.516Step-by-step explanation: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