Discuss the below:
Q(a) Explain what you understand by the following:
(i) Unbiasedness
(ii) Efficiency
(iii) Consistency
(b) A survey of a random sample of 250 car commuters indicates that 80 would switch to commuting by public transport if they had to pay at least $10 per week for parking at their work places.
(i) Using a 95% confidence level, calculate the confidence interval for the proportion of the commuters who might be expected to change to using public transport for the journey-to-work.
(ii) Comment on the relationship between sample size and margin of error.
(c) Suppose we want to estimate, with 95% confidence, the percentage of commuters who would change to using public transport for the journey-to-work with a margin of error of +-3%. How large a sample of people will need to be taken:
(i) A preliminary estimate suggests that the true percentage is about 32%.
(ii) No preliminary estimate is available.