Sampled Subdivision Number of Mean Bonus Clerical Employees (Dollars) 1 69 83 75 64 3 41 42 4 36 108 59 136 6. 82 102 64 95 8 71 98 2.
A union executive wants to estimate the
a. Find a point estimate of the population mean bonus per clerical employee for this month.
b. Find a 99% confidence interval for the population mean.
Given:
A union executive wants to estimate the mean value of bonus payments made to a corporation's clerical employees in the first month of a new plan. This corporation has 52 subdivisions, and a simple random sample of 8 of these is taken. Information is then obtained from the payroll records of every clerical worker in each of the sampled subdivisions. The results obtained are shown in the attached table:
a. Find a point estimate of the population mean amount of time that televisions are in use in this city.
b. Find a 90% confidence interval for the population mean.
It follows the cluster sampling that involves the mean population estimation. It involves the population being subdivided into K clusters that follows the simple random sampling technique. It follows n1, n2_...nk values based on the population size that is being selected at K clusters. The equation as follows,
Here,
The cluster size is denoted by n
The cluster population mean value being K
The equation as follows,
Here,
It follows the unbiased estimators that determine the overall population that includes the mean and variance that follows the population mean. The formula is given as,
The value follows the 100(1 - α) %based on the confidence interval with the population mean based on the cluster sampling as follows,
The average time amount in a week involves the television sets that includes the house hold city value with K = 65 precincts. Hence the cluster sampling plan was considered. The value of sample is said to be k=10 precincts yielding the result.
Step by step
Solved in 8 steps with 12 images
