Example 2 Listed below are the number of years it took for a random sample of college students to earn bachelor s degrees Construct a 95 confidence interval estimate of the mean time required for all college students to earn bachelor s degrees Does the confidence interval contain the value of 4 years Is there anything about the data that would suggest that the confidence interval might not be a good result Assume the data is normally distributed 4 4 4 4 4 4 4 5 4 5 4 5 4 5 4 5 6 6 8 9 9 13 13 15 Use calculator or software to calculate sample mean and sample standard deviation n x S S 1a 2 n Margin of Error E 1 a 2 df Confidence interval x E