For a variable with = 25.00, how large should the sample be for a desired 95% confidence interval width of 15?
A) 7
B) 11
C) 43
D) 121

Question

For a variable with  = 25.00, how large should the sample be for a desired 95% confidence interval width of 15?
A) 7 
B) 11 
C) 43 
D) 121

Quizplus · Accepted Answer

The sample size needed for a 95% confidence interval with a width of 15 is given by:
n = (Zα/2 * σ / E)^2
where Zα/2 is the critical value of the standard normal distribution for 95% confidence (which is 1.96), σ is the population standard deviation (which is unknown, so we will assume a conservative estimate of 10), and E is the margin of error, which is half the desired width of the confidence interval (so E = 15/2 = 7.5).

Plugging in these values, we get:
n = (1.96 * 10 / 7.5)^2
n = 42.95

Since we cannot have a fractional sample size, we round up to the nearest integer to get a sample size of 43. Therefore, the best answer choice is C.

For a Variable with = 25