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 population standard deviation of 3 hours, what is the required sample size if the error should be less than ½ hour with a 99% level of confidence?
A) 196
B) 240
C) 15
D) 16

Question

Quizplus · Accepted Answer

The formula to calculate the sample size is:

n = ((Z-value * population standard deviation) / margin of error)²

Here, the population standard deviation is given as 3 hours, and the margin of error, E = 0.5 hours.

The Z-value for a 99% confidence level is 2.576 (from the standard normal distribution table).

Substituting these values in the formula, we get:

n = ((2.576 * 3) / 0.5)²
n = 239.93

Round up to the nearest whole number, we get the required sample size as 240.
Therefore, the choice B is the correct answer.

A Group of Statistics Students Decided to Conduct a Survey