A group of statistics students decided to conduct a survey at their university to find the average (mean) amount of time students spent studying per week. Assuming a standard deviation of 3 hours, what is the required sample size if the error is to be less than ½ hour with a 99% level of confidence?
A) 196
B) 240
C) 15
D) 16

Question

Quizplus · Accepted Answer

To find the required sample size, we use the formula:

n = (Z^2 * σ^2) / E^2

Where,
Z = Z-score at 99% level of confidence = 2.576 (from the Z-table)
σ = standard deviation = 3
E = margin of error = 0.5

Substituting the values, we get:

n = (2.576^2 * 3^2) / 0.5^2
n = 239.7

Rounding up to the nearest integer, the required sample size is 240. Therefore, the best choice is option B.

A Group of Statistics Students Decided to Conduct a Survey