Problem 2 - Feasibility of a canteen facility

An appliance factory in the United States would like to estimate how much its factory workers spend per week to purchase lunch meals.This is to help in determining whether it would be worthwhile to open and operate its own canteen facility.The Chief Operating Officer was advised by a senior data analyst that spending per week on lunch meals follows a normal distribution.A random sample of 36 workers who purchase lunch meals were surveyed.It revealed that on average they paid $95 per week in buying lunch meals with a standard deviation equal to $11.5.Estimate with 95% confidence the actual mean spending on lunch meals per week for all of the factory workers.

a)Suppose you were a junior data analyst working for the factory.Which formula would you select to use in solving the problem?Provide a brief reason on your selection. 1 mark

b)Obtain the lower confidence limit and the upper confidence limit of the 95% confidence interval estimate of the mean spending on lunch meals per week for all of the factory workers. Display working. 3 marks

c)Present an interpretation of the lower confidence limit and the upper confidence limit obtained in part b) in the context of the problem. 1.5 marks

d)Experience shows that operating canteen facilities in factories would be worthwhile if workers spend more than $100 per week on average to purchase lunch meals.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 Chief Operating Officer of the factory on whether or not it should open its own canteen facility. Yes or no? Why?1.5 marks

e)What would happen to the width of the interval when there is an increase in the value of the standard deviation?Assume all of the other variables to do the calculation of confidence interval held constant. 1 mark