A random sample of 100 boxes of cereal had a sample mean weight of 396 grams. The standard deviation is known to be 5 grams. The upper end of the confidence interval for the mean is 405.8 grams.

Question

Quizplus · Accepted Answer

The upper end of a confidence interval for the mean is calculated using the formula: $\bar{x} + z\frac{\sigma}{\sqrt{n}}$, where $\bar{x}$ is the sample mean, $z$ is the z-score corresponding to the desired confidence level, $\sigma$ is the population standard deviation, and $n$ is the sample size. Given the sample mean ($396$ grams), standard deviation ($5$ grams), and sample size ($100$), the upper end of the confidence interval would not reach $405.8$ grams without knowing the specific confidence level and corresponding z-score. However, even with a high confidence level (e.g., 99% with a z-score around 2.58), the increase from the sample mean due to the margin of error would not be nearly $9.8$ grams ($405.8 - 396$).

A Random Sample of 100 Boxes of Cereal Had a Sample