The document discusses determining sample sizes from different populations using stratified proportionate sampling. It provides population data on lecturers, readers, and professors categorized by their length of service. It also provides a formula and example for calculating sample size based on desired precision, population mean and standard deviation, and sample mean. The goal is to determine appropriate sample sizes that represent the ratios in the overall populations and achieve a desired level of precision while minimizing cost.

3. Sampling Design Process

6. Sample Size Determination

7. Find how many lecturers, readers, & professors would be selected from each category if,
• We follow stratified proportionate sampling method & take 10 % of the universe equivalent to the
sample size,
• If the size of the sample is 10 % of the universe, but the lecturers, readers, & professors are to be in
the ratio of 5 : 3 : 2 and weightage of the length of service is to be in the ratio of 4 : 3 : 2 : 1.
Length of Service Lecturers Readers Professors Total
Less than 5 years 2000 250 50 2300
5-10 years 3000 220 80 3300
10-15 years 1500 170 30 1700
More than 15 years 880 80 40 1000
Total 7380 720 200 8302

8. Sample Size Determination
2D
2σ2Z
n 
n = sample size
Z= value at a specified level of confidence or desired level of precision
σ = Standard Deviation of the population
D = difference between population mean and sample mean
Determine the sample size, if S.D. of the population = 6, population mean = 25, sample mean =
23, and the desired degree of precision is 99 % (Z-value at 1% significance level is 2.576).
Standard error of mean (σx)
Standard error of Proportion (σp)

9. Precision
Cost