A quality control analyst wants to estimate the actual amount of glue contained in 2-litres cans produced from a well-known manufacturer. It is known from the manufacturer's specifications that the standard deviation of the amount of glue is equal to 0.04 litres. A random sample of 80 cans is selected, and the sample mean amount of glue per 2-litre can is 1.990 litres.
1.1 Set up a 99% confidence interval estimate of the true population mean amount of glue contained in a 2-litre can.
1.2 On the basis of your results, do you think that the quality control analyst has a right to complain to the manufacturer? Why?
1.3 Does the population amount of glue per can have to be normally distributed here? Explain.
1.4 Explain why an observed value of 1.96 litres for an individual can is not unusual, even though it is outside the confidence interval you calculated.
1.5 Suppose that you used a 95% confidence interval estimate. What would be your answers to 1.1 and 1.2?