Problem 1 - Efficiency analysis of workflow system(8 marks)

John is the Chief Financial Officer of a very large software company that employs more than 5,000 programmers.He is committed to increase funding to the development of the company's new workflow system if at least 20% of his programmers agree that the system significantly enhances their work efficiency.700 programmers were randomly selected and surveyed for this analysis.175 programmers stated that they find the workflow system is useful and boost their work efficiency.Estimate with 99% confidence the proportion of all of the company's programmers who find the new workflow system useful for their work efficiency.

a)Suppose you were a researcher working for the data analytic department of the company.Which formula would you select in solving the problem?Provide a brief reason on your selection.1 mark

x = 175 n = 700

b)Obtain the lower confidence limit and the upper confidence limit of the 99% confidence interval estimate of the proportion of all the company's programmers who find the new workflow system useful for their work efficiency.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)Based on the interval estimation you just conducted, present brief statements of two or three sentences for John, the Chief Financial Officer.Should he allocate more funding for the development of the company's new workflow system? Yes or no? Why?1.5 marks

e)What would happen to the width of the interval when a lower sample size is used?Assume all of the other variables to do the calculation of confidence interval held constant. 1 mark