Question

A company would like to estimate how much its employees pay in childcare costs per month in order to decide whether it would be worthwhile to provide day care facilities to its employees. The company was advised by a statistician that childcare cost per month historically follows a normal distribution. A random sample of 25 employees who use childcare services revealed that on average they paid $300 per month in childcare costs with

a standard deviation equal to $10. Estimate with 90% confidence the actual mean monthly childcare expenses for all employees.

a) You were recently hired as a junior data analyst working for the company. Specify the appropriate formula you would use to solve the problem. Provide a brief reason why you chose the formula. 1 mark

b) Obtain the 90% confidence interval estimate of the mean monthly childcare expenses for all employees. Display working. 3 marks

c) Provide an interpretation of the answers you obtained in part b) in the context of the problem. 1.5 marks

d) Experience shows that providing day care facilities would be worthwhile if employees spend more than $310 in child care costs per month. Taking into consideration this statement and the results of the estimation you conducted in part b), present brief statements of two or three sentences to the company management on whether or not it should open its own day care facilities. Yes or no? Why? 1.5 marks

e) Assuming all of the other variables to do the calculation of confidence interval held constant, what would happen to the width of the interval when a higher sample size is used?

Answer 1