For a variable with = 15.00, how large should the sample be for a desired 95% confidence interval width of 6?
A) 10
B) 24
C) 96
D) 576

Question

For a variable with  = 15.00, how large should the sample be for a desired 95% confidence interval width of 6?
A) 10 
B) 24 
C) 96 
D) 576

Quizplus · Accepted Answer

In order to calculate the required sample size, we need to use the formula for margin of error:

Margin of error = z*(sigma/sqrt(n))

Where z is the z-score corresponding to the desired level of confidence, sigma is the population standard deviation (which we don't know, so we'll use a conservative estimate of 10), and n is the sample size.

We want the margin of error to be no more than 6, so we can set up the following inequality:

6 = z*(10/sqrt(n))
sqrt(n) = z*(10/6)
n = (z*(10/6))^2

Since we want a 95% confidence interval, the z-score is 1.96. Plugging this in, we get:

n = (1.96*(10/6))^2
n = 96.04

Rounding up, the required sample size is 97, which is closest to choice C: 96.

For a Variable with = 15