[7 marks]

a)A small winery is considering expanding and buying a vineyard. They want to determine mean yield relative to cost. From a sample of 30 vineyard sites, the mean yield is 1kg per dollar with a standard deviation of 0.30.

Constructand interpret a 95% confidence interval for the population mean yield for a vineyard.

For full marks, clearly identify the formula you are using (you can refer to its number on the formula sheet).

b)Market analysis revealed that the expansion would be profitable only if the average yield didn't exceeded a yield of 1.05. Given the confidence interval you have constructed, should the winery expand and buy a vineyard? Justify your answer briefly.