Question 4

Part I Theoretical Discussion(50%)

a)Discuss stratified random sampling

b)Discuss central limit theorem and its importance

c)Discuss main biases in sampling

Part II Computation(50%)

a)It has been determined that the average time taken by customers to fill a customer satisfaction survey follows non-normal distribution with unknown variance. In a sample of 61 customers the average time taken to fill a customer satisfaction survey was 24 minutes with standard deviation of 8 minutes. On this basis, estimate the average time taken by customers to fill a customer satisfaction survey using the 95% confidence level.

b)From past experience, it is known that the average expenditure per visit to a corner shop is normally distributed with a standard deviationof 2.50. How large a sample should be taken to be within 0.50 of the actual average with 90% confidence? (assume that Z-score for 90% confidence interval is 1.645).