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

Question

Quizplus · Accepted Answer

To find the required sample size for estimating the mean with a specific margin of error, the formula is $n = \left(\frac{Z \cdot \sigma}{E}\right)^2$, where $Z$ is the Z-score corresponding to the confidence level, $\sigma$ is the population standard deviation, and $E$ is the margin of error. For a 95% confidence level, $Z = 1.96$, $\sigma = 6$ hours, and $E = 0.5$ hours. Plugging these values into the formula gives $n = \left(\frac{1.96 \cdot 6}{0.5}\right)^2 = 553.44$, which rounds up to 554.

A Group of Statistics Students Decided to Conduct a Survey