Question 2 [15] In a random sample of 200 Small Medium Enterprises (SMES) operating in Katutura,...

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Question 2 [15] In a random sample of 200 Small Medium Enterprises (SMES) operating in Katutura, it was found that 68 do not have licenses from the local authority. Required: a) Construct and interpret a 95% confidence interval for the population proportion of SMES operating in Katutura who have licenses from the local authority. (10) b) Suppose the sample size is decreased. What will happen to the answer in (a)? Motivate your answer. (5) Question 3 [25] Heita, a kapana vendor at a local open market reported that his average monthly profit is less than N$ 2 100. Heita's business partner is however arguing that Heita is deliberately underestimating his average monthly profit. Suppose Heita's monthly profits for a period of six months are as follows: Month 1 2 3 4 5 Profit (NS) 2 200 2 000 2 000 1 800 2 200 2 100 Required: a) Use the critical value approach and test the hypothesis at a 1% level of significance. What conclusion can be made about Heita's monthly profit and his business partner's argument? Show all the hypothesis test steps. (25) Question 2 [15] In a random sample of 200 Small Medium Enterprises (SMES) operating in Katutura, it was found that 68 do not have licenses from the local authority. Required: a) Construct and interpret a 95% confidence interval for the population proportion of SMES operating in Katutura who have licenses from the local authority. (10) b) Suppose the sample size is decreased. What will happen to the answer in (a)? Motivate your answer. (5) Question 3 [25] Heita, a kapana vendor at a local open market reported that his average monthly profit is less than N$ 2 100. Heita's business partner is however arguing that Heita is deliberately underestimating his average monthly profit. Suppose Heita's monthly profits for a period of six months are as follows: Month 1 2 3 4 5 Profit (NS) 2 200 2 000 2 000 1 800 2 200 2 100 Required: a) Use the critical value approach and test the hypothesis at a 1% level of significance. What conclusion can be made about Heita's monthly profit and his business partner's argument? Show all the hypothesis test steps. (25)