The grade point averages for 10 randomly selected junior college students are 2.0, 3.2, 1.8, 2.9, 0.9, 4.0, 3.3, 2.9, 3.6, 0.8. Assume the grade point averages are normally distributed. What is the 98% confidence interval for the true mean?
1 Answer
One way to calculate the confidence interval of a sample mean is to use the student's t-distribution to find that with
Explanation:
One way to calculate the confidence interval of a sample mean is to use the student's t-distribution where the limits of the interval are given by:
where
First we need the sample mean and sample standard deviation:
and the sample standard deviation:
Plugging these values into our first equation we can calculate the limits of the confidence interval for our mean:
Where we can look up the value of
therefore we can say with