The unemployment rate of persons with a disability is typically higher than for those with no disability.Recent statistics report that the national rate of unemployment among
This group is 14.5%.The local government of a small city wants to determine the rate in
Its region to within ±5 with 95% confidence.How many individuals with disabilities
Should they sample?
A)135
B)191
C)354
D)678
E)981

Question

The unemployment rate of persons with a disability is typically higher than for those with no disability.Recent statistics report that the national rate of unemployment among
This group is 14.5%.The local government of a small city wants to determine the rate in
Its region to within ±5  with 95% confidence.How many individuals with disabilities
Should they sample?
A)135 
B)191 
C)354 
D)678 
E)981

Quizplus · Accepted Answer

To calculate the sample size needed for this study, we use the formula:

n = (Zα/2)² * p̂ * (1-p̂) / ME²

Where: 
- Zα/2 = 1.96 for a 95% confidence level 
- p̂ = the estimated proportion of individuals with disabilities who are unemployed (we don't have this information, so we assume it to be equal to the national rate of 14.5%) 
- ME = the margin of error, which we want to be ±5%, or 0.05

Plugging in the values:

n = (1.96)² * 0.145 * (1-0.145) / 0.05² = 190.89

Rounding up to the nearest whole number, we get a sample size of 191. Therefore, the best choice is B, sampling 191 individuals with disabilities.

The Unemployment Rate of Persons with a Disability Is Typically