Suppose that a survey was commissioned by the Ministry of Finance in order to determinethe income of local vendors as part of their project aimed at investigating the feasibility of the presumptive tax. A sample of 26 local vendors was selected and their sample mean monthly income and variance were found to be N$ 7 600 and 1 250 (N$ squared), respectively.

a) What is the 90% confidence interval estimate for the population mean monthly income of the local vendors

b) Provide an interpretation of the answer in a).

c) What can be done to improve the precision of the confidence interval estimate in a)? Discuss.

d) A representative of the local vendors argues that the local vendors 'average monthly income is not more than N$ 7 500. Conduct a hypothesis test at a 2.5% level of significance to determine the validity of the claim made by the local vendors' representative. Show all hypothesis test steps. (10)

e) If the hypothesis test in d) was to be conducted at a level of significance greater than 2.5%, what will be the conclusion? Motivate.

f) Explain the reasons for hypothesis testing using a practical example.