In: Statistics and Probability
Registrar’s Office members design a study of students’ performance. They believe that individual course grades measured in a 100-point scale are normally distributed with the population standard deviation = sigma = 19 points. The goal is to estimate the population mean with the interval no wider than 9 points.
1. Set confidence level = C = 0.99 and find the smallest number of records required for the study goals.
2. Will a sample of n = 100 records guarantee that the interval is no wider than 9 points? Explain your answer.
3. Using confidence level = C = 0.95, find the smallest number of records required for this study.
4. Will the sample of n = 81 guarantee that the interval is no wider than 9 points? Explain your answer.