A random sample of 60 business students required an average of 50.7 minutes to complete a statistics exam. Assume that the population standard deviation to complete the exam was 10.4 minutes. The 98% confidence interval around this sample mean is____ .
A)(47.6, 53.8)
B)(45.4, 56.0)
C)(49.8, 51.6)
D)(48.9, 52.5)

Question

Quizplus · Accepted Answer

To calculate the 98% confidence interval for the mean, we use the formula: $\bar{x} \pm Z \frac{\sigma}{\sqrt{n}}$, where $\bar{x}$ is the sample mean, $Z$ is the Z-score corresponding to the confidence level, $\sigma$ is the population standard deviation, and $n$ is the sample size. For a 98% confidence level, the Z-score is approximately 2.33. Plugging in the values: $50.7 \pm 2.33 \times \frac{10.4}{\sqrt{60}}$, we get the interval (47.6, 53.8).

A Random Sample of 60 Business Students Required an Average