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 6 hours, what is the required sample size if the error is to be less than ½ hour with a 95% level of confidence?
A) 554
B) 130
C) 35
D) 393

Question

Quizplus · Accepted Answer

The required sample size can be calculated using the formula for the sample size of a mean, $n = \left(\frac{Z\sigma}{E}\right)^2$, where $Z$ is the Z-score corresponding to the confidence level (1.96 for 95%), $\sigma$ is the standard deviation (6 hours), and $E$ is the margin of error (0.5 hours). Plugging in the values, $n = \left(\frac{1.96 \times 6}{0.5}\right)^2 = 553.44$, which rounds up to 554.

A Group of Statistics Students Decided to Conduct a Survey