The Department of Trade and Industry (DTI) conducted a survey to estimate the average number of employees per small and medium-sized enterprises (SME) in Gauteng. A random sample of 144 SMEs in Gauteng found that the average number was 24.4 employees. Assume that the population standard deviation is 10.8 employees and that the number of employees per SME is normally distributed.
(a) Estimate, with 95% confidence, the actual average number of employees per SME in Gauteng. Interpret the findings for the DTI. Use the z-table.
(b) Compute the confidence interval in (a) using Excel's NORMSINV formula to find the z-value.
(c) Compute the confidence interval in (a) using Excel's CONFIDENCE formula.