Give a reason why, in carrying out a statistical investigation, a sample rather than a complete population may be used.
Rose wishes to investigate whether men in her town have a different life-span from the national average of 71.2 years. She looks at government records for her town and takes a random sample of the ages of 110 men who have died recently. Their mean age in years was 69.3 and the unbiased estimate of the population variance was 65.61.
(a) Calculate a \(90 \%\) confidence interval for the population mean and explain what you understand by this confidence interval.
(b) State with a reason what conclusion about the life-span of men in her town Rose could draw from this confidence interval.