Suppose that there are two independent random samples of it, and observations from normally distributed populations with means, and and variances and art. If the observed sample means are and then a 100(1-% confidence interval for the difference between two means, independent samples, and known population variances is given by 2199 183 of, equivalently (T- ME where the margin of error, ME, I given by the following: ME In some applications, historical variances from similar studies can be used as the true population variances. u49 Example 8.3 Comparison of GPAS (Confidence Interval) From a very large university, independent random samples of 120 students majoring in marketing and 90 students majoring in finance were selected. The mean GPA for the random sample of marketing majors was found to be 3.08, and the mean GPA for the random sample of finance majors was 2.88. From similar past studies the population standard deviation for the marketing majors is assumed to be 0.42 similarly, the popu- lation standard deviation for the finance majors is 0.61. Denoting the population mean for marketing majors by A- and the population mean for finance majors by find a 95% confidence interval for)