v5 On taking the square root, @r, = 1.85 Thus, the 95% confidence interval for the mean number of orders per restaurant re- ceived in a week is 20.1 + (1.96)(1.85) The 95% confidence interval runs from 16.5 to 23.7 orders per restaurant. Since the population total is the product of the population mean and the number of population members, these procedures can be readily modified to allow its estimation, as described next. Estimation of the Population Total Using Stratified Random Samples Suppose that random samples of n, individuals from strata containing Ni individuals (j = 1,2,...,K) are selected and that the quantity to be estimated is the population total, Nu. 1. An unbiased estimation procedure for Nu leads to the following point estimate: NX, = NT; (17.5) 2. An unbiased estimation procedure for the variance of our estimator of the population total yields the following estimate: Not - Nor (17.6) 3. Provided the sample size is large, a 100(1 a)% confidence interval estimation of the population total using stratified random samples is obtained from the following: Ny + 2a/2N (17.7) Example 17.2 Total Annual Enrollment in Business Statistics (Estimation) The publisher of a business statistics text wants an estimate of the total number of stu- dents taking business statistics courses in all U.S. colleges. Suppose that there are 1,395 colleges in the United States, 364 have 2-year programs and 1,031 are 4-year schools. A simple random sample of 40 two-year schools and an independent simple random sample of 60 four-year schools were taken. The sample means and standard deviations of numbers of students enrolled in the past year in business statistics courses are given in the table. Estimate the total annual enrollment in business statistics courses. Mean Standard deviation 2-YEAR SCHOOLS 154.3 87.3 4-YEAR SCHOOLS 411.8 219.9