The personnel manager of a corporation wants to estimate, tor one year, the tota

ID: 3131465 • Letter: T

Question

The personnel manager of a corporation wants to estimate, tor one year, the total number of days used for sick leave among all 46 plants in his firm. The 46 plants are divided into 20 "small" plants and 26 "large" plants. From past experience, the manager figures that the small plants may use from 0 to 100 days of sick leave, whereas the large plants may use from 10 to 200 days of sick leave. If he desires to estimate the total to within 100 days: Find the appropriate allocation of the sample to the two strata. Find the appropriate sample size.

Explanation / Answer

Sampling

Solution a)

Here, we have to find appropriate allocation for the given two strata.

We are given

Total plants = 46

Small plants = 20

Large plants = 26

For the small plants, we need to total percentage of observations from sample given as below:

Total percentage = (20/46)*100 = 43.48%

Now, we have to find the percentage for allocation of the large plants which is given as below:

Total percentage = (26/46)*100 = 56.52%

Solution b)

Here, we have to find the appropriate sample size

Sample Size Determination

Data

Estimate of True Proportion

0.434783

Sampling Error

0.1

Confidence Level

95%

Intermediate Calculations

Z Value

-1.9600

Calculated Sample Size

94.4026

Result

Sample Size Needed