A professor wants to use the mean of a random sample to estimate the average amount of time students take to do their homework. He wants to be able to assert with a probability of 0.99 that his error will be at most 15 minutes. If $\sigma=29$ minutes, how large a sample will he need?
A) 15
B) 14
C) 25
D) 4

Question

Quizplus · Accepted Answer

To estimate the sample size needed, the formula $n = \left(\frac{Z\sigma}{E}\right)^2$ is used, where $Z$ is the Z-score corresponding to the desired confidence level (0.99 in this case, which corresponds to a Z-score of approximately 2.576), $\sigma$ is the population standard deviation (29 minutes), and $E$ is the margin of error (15 minutes). Plugging in the values, $n = \left(\frac{2.576 \times 29}{15}\right)^2 \approx 25.1$. Since the sample size must be a whole number, rounding up gives 25.

A Professor Wants to Use the Mean of a Random σ=29\sigma=29σ=29

A Professor Wants to Use the Mean of a Random $\sigma=29$