question 1

Instructions: Answer ALL questions. For calculation, give the value up to 4 decimal places with unit. A quality controller measured the volume of perfume for a sample of 40 bottles from a-day production. Based on the sample, the mean volume of the perfume is 12.5286 ml with standard deviation of 1.45 ml. Assume that the data is normally distributed. i) Identify the variable in the study. (1 Mark) ii) Construct a 95% confidence interval for population mean of volume of the perfume. Interpret the result. (7 Marks) iii) Find the confidence limit of the confidence interval in (ii). (2 Marks) iv) Find the estimation error of the confidence interval in (ii). (1 Mark) V) How many bottles of the perfume must be sampled so that at least 95% confidence interval will specify the population mean to estimation error of 0.05? (5 Marks) vi) Construct a one-sided lower bound of 95% confidence interval for population mean of volume of the perfume. (4 Marks)