TABLE 8-3
To become an actuary, it is necessary to pass a series of 10 exams, including the most important one, an exam in probability and statistics. An insurance company wants to estimate the mean score on this exam for actuarial students who have enrolled in a special study program. They take a sample of 8 actuarial students in this program and determine that their scores are: 2, 5, 8, 8, 7, 6, 5, and 7. This sample will be used to calculate a 90% confidence interval for the mean score for actuarial students in the special study program.
-Referring to Table 8-3, it is possible that the confidence interval obtained will not contain the mean score for all actuarial students in the special study program.

Question

Quizplus · Accepted Answer

The table provides critical values for different levels of confidence and sample sizes. However, the sample size in this problem is small (n=8), so we cannot use the table directly. Instead, we need to use the t-distribution with n-1 degrees of freedom. This means that the confidence interval will be based on the sample mean, the sample standard deviation, and the t-value corresponding to a 90% confidence level and 7 degrees of freedom (df=n-1). Since we don't know the population mean for all actuarial students in the special study program, it is possible that the confidence interval obtained from this sample will not contain the true value. This is because there is random variation in the sample mean from one sample to another, and the confidence interval is based on a margin of error that accounts for this uncertainty. Therefore, there is a chance that the true mean score for actuarial students in the special study program is outside the interval calculated from this sample.

TABLE 8-3 to Become an Actuary, It Is Necessary to Pass a Pass