At Abraham Lincoln High School a popular achievement test is used for college placement. Counselors selected a random sample of 41 students from Abraham Lincoln High School and scored their tests by hand before sending them in for computer processing. for this sample, the sample mean is 95 and the sample standard deviation is 12. Construct a 99% confidence interval for μ, the population mean score for Abraham Lincoln High.
Now, it is believed that the standard deviation of the test score for Abraham Lincoln High School is 9, construct a 95% confidence interval for μ, the population mean score for Abraham Lincoln High.