A random sample of 25 third graders scored an average of 3.2 on a standardized reading test. The standard deviation was 0.95. Calculate a 99% confidence interval for the mean score on this test.
A) (3.01, 3.39)
B) (2.49, 3.91)
C) (2.81, 3.59)
D) None of the above

Question

Quizplus · Accepted Answer

The correct confidence interval must be calculated using the formula for a confidence interval for the mean, which is $\bar{x} \pm z\frac{\sigma}{\sqrt{n}}$, where $\bar{x}$ is the sample mean, $z$ is the z-score corresponding to the desired confidence level, $\sigma$ is the standard deviation, and $n$ is the sample size. For a 99% confidence level, the z-score is approximately 2.576. Plugging in the given values ($\bar{x} = 3.2$, $\sigma = 0.95$, $n = 25$), the calculation does not match any of the provided options exactly, indicating the correct answer is "None of the above."

A Random Sample of 25 Third Graders Scored an Average