Question

Thirty (30) randomly selected students took a calculus final. If the sample mean was 83 and the sample standard deviation was 13.5find a 99% confidence interval for the mean score of all calculus students taking this test.

Answer 1

To find the 99% confidence interval for the mean score, use the formula: Confidence Interval = sample mean ± (critical value)(sample standard deviation / √sample size). Substituting the values, we get a confidence interval of (74.183, 91.817).

Step-by-step explanation:

To find the 99% confidence interval for the mean score of all calculus students taking the test, we can use the formula:

Confidence Interval = sample mean ± (critical value)(sample standard deviation / √sample size)

First, we need to find the critical value using the Z-table for a 99% confidence level. The critical value for a 99% confidence level is approximately 2.576.

Substituting the values into the formula, the confidence interval is:

83 ± (2.576)(13.5 / √30)

Simplifying the expression, we get:

83 ± (8.817)

Therefore, the 99% confidence interval for the mean score of all calculus students taking the test is (74.183, 91.817).