Question

Some years ago a small university did an SRS survey of students that graduated 20 years previously to find out their current income. From that data it found the income graduates had 20 years after they graduated varied between degrees. Because the number of students graduating 20 years ago varies by degree it was decided a stratified sample should be done this year to improve the precision of the analysis. The five degrees are listed below with the number of students who graduated in 1999 along with the estimated variance of the responses for each strata based on the last survey’s responses.

Strata Number	Population in Strata	Variance of Strata
Arts	131	632,562,265
Science	84	1,140,398,914
Liberal Arts	53	654,465,304
Cultural Studies	32	102,749,044
Management	12	10,838,799,963

This year the investigators can afford to survey 40 graduates from 1999.

1. Calculate the sample size for each strata and sample error at 95% confidence level if the number sampled for each strata is the same.
2. Use proportional allocation to calculate the number to be sampled in each strata. Calculate the sample error at the 95% confidence level.
3. Using Neyman allocation (the cost to sample a unit in any strata is the same) to calculate the number to be sampled in each strata. Calculate the sample error at the 95% confidence level.
4. Explain why the results for the sample error in a), b) and c) are different.
5. Normally the variance of the variable y we are measuring is not known so we cannot stratify using it. Instead we often use the variance for an auxiliary variable which is known for all units. If there were several possible auxiliary variables available explain how you would choose which one to use.

Please answer all questions

Answer 1