CAIE S2 2015 June — Question 5

Exam BoardCAIE
ModuleS2 (Statistics 2)
Year2015
SessionJune
TopicHypothesis test of a normal distribution

5 The masses, \(m\) grams, of a random sample of 80 strawberries of a certain type were measured and summarised as follows. $$n = 80 \quad \Sigma m = 4200 \quad \Sigma m ^ { 2 } = 229000$$
  1. Find unbiased estimates of the population mean and variance.
  2. Calculate a 98\% confidence interval for the population mean. 50 random samples of size 80 were taken and a \(98 \%\) confidence interval for the population mean, \(\mu\), was found from each sample.
  3. Find the number of these 50 confidence intervals that would be expected to include the true value of \(\mu\).