Practice
- A nutritionist wants to estimate the average number of cups of coffee consumed per week by graduate students. A random sample of 16 students shows a mean of 9.3 cups with a sample standard deviation of 2.1 cups. Construct a 90% confidence interval for the true mean weekly coffee consumption of graduate students.
Solution
From the problem we get the following information:
- A confidence level of 90%
- Sample Size is \(n=16\)
- The sample mean is \(\bar{x} = 9.3\)
- The sample standard deviation is \(s=2.1\)
First, we verify the central limit theorem.
- Is the sample random? Yes (stated in the problem)
- Is the sample large enough? No (sample size is smaller than 30)
- If it’s not large enough, is the population normally distributed? No (not stated in the problem)
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