Scientists want to estimate the mean weight gain of mice after they have been fed a special diet. From previous studies, it is known that the weight gain is normally distributed with standard Deviation 2 grams.
How many mice must be weighed so that a 99% confidence interval for mean weight will have a margin Of error of 0.4 grams?
A) 26
B) 1
C) 13
D) 166

Question

Quizplus · Accepted Answer

To find the sample size needed for a given margin of error in a confidence interval, we use the formula: $n = \left(\frac{Z \cdot \sigma}{E}\right)^2$, where $n$ is the sample size, $Z$ is the Z-score corresponding to the desired confidence level, $\sigma$ is the population standard deviation, and $E$ is the margin of error. For a 99% confidence interval, the Z-score is approximately 2.576. Given $\sigma = 2$ grams and $E = 0.4$ grams, substituting these values gives $n = \left(\frac{2.576 \cdot 2}{0.4}\right)^2 \approx 166$.

Scientists Want to Estimate the Mean Weight Gain of Mice