In all answers show your calculations (Except variance calculation). But full points will be given to the correct answer). The answers without the way of calculations will affect the grade.

Question 4) Miscellaneous practical and theoretical questions (30%)

1. Assume you have observed 30 shops during a day and found that average sales is 2000 and known sample variance is 1200, respectively. Find 99% confidence interval for the population average of the sales. (8%)

1. One of the Manager in the Shop advise us CEO to to use 88% confidence interval instead of 99% for the population mean. Provide comments on result you found and compare it with the result in part c). (10%)

1. Explain what is meant by “Unbiased” and “Efficient” estimator. Give an example of each when you provide your answer. (6%)

1. Define Central Limit Theorem and Law of Large Numbers in your own words and also referring to the discussions we made in class (6%)

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