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In: Statistics and Probability

A sample of size 30 students is to be drawn from a population consisting of 300...

A sample of size 30 students is to be drawn from a population consisting of 300 students belonging to two colleges A and B. the mean and standard deviations of their marks are given below:

Strata

Total number of students Ni

Mean

Standard deviation σi

College A

200

30

10

College B

100

60

40

Total

300

90

50

  1. How would you draw the sample using proportional allocation techniques? Hence, obtain the variance of the estimate of the population mean and compare its efficiency with simple random sampling without replacement (SRSWOR).
  2. Variance of the estimate of the population mean for simple random sampling without replacement (SRSWOR).
  3. Variance of the estimate of the population mean for proportional allocation
  4. 95% confidence interval of the population mean for proportional allocation.

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