Pleas need solve 5.2 A corporation desires to estimate the total number of worke
ID: 3173605 • Letter: P
Question
Pleas need solve 5.2 A corporation desires to estimate the total number of worker-hours lost, for a given month, because of accidents among all employees. Because laborers, technicians, and administrators have different accident rates, the researcher decides to use stratified ran- dom sampling, with each group forming a separate stratum. Data from previous years suggest the variances shown in the accompanying table for the number of worker-hours lost per employee in the three groups, and current data give the stratum sizes. Determine the Neyman allocation for a sample of n 30 employees.Explanation / Answer
The first step is to decide how to allocate sample in order to maximize precision. Based on Neyman allocation, the best sample size for stratum h is:
nh = n * ( Nh * h ) / [ ( Ni * i ) ]
Our sample h is going to be laborers (first)
nlaborers = 30(132 * 6)/[(132*6)+(92*5)+(27*3)] = 17.82
ntechicians = 30(92*5)/[1333] = 10.35
nadministrators = 30(27*3)/[1333] = 1.82
So for a sample size of 30 employees, we should have 18 laborers, 2 administrators and 10 technicians for maximum precision accuracy