MATH 1040 - Introduction to Statistics

Practice

A professor surveys 41 students about how many hours they studied for the last exam. The sample mean is 14.2 hours, and the sample standard deviation is 4.6 hours. Construct a 95% confidence interval for the true mean number of hours students studied for the exam.

Solution

From the problem we get the following information:

• A confidence level of 95%
• Sample Size is \(n=41\)
• The sample mean is \(\bar{x} = 14.2\)
• The sample standard deviation is \(s=4.6\)

First, verify the central limit theorem

• Is the sample random? No (We cannot assume this from the problem)
• Is the sample large enough? Yes (sample size is at least 30)

At this point, we can’t solve the problem because the Central Limit Thereom does not hold.

See the solution if the problem is modified so the CLT holds

Return back to Lesson 18.5