CAIE S2 2017 June — Question 4

Exam BoardCAIE
ModuleS2 (Statistics 2)
Year2017
SessionJune
TopicHypothesis test of a normal distribution

4 Last year the mean level of a certain pollutant in a river was found to be 0.034 grams per millilitre. This year the levels of pollutant, \(X\) grams per millilitre, were measured at a random sample of 200 locations in the river. The results are summarised below. $$n = 200 \quad \Sigma x = 6.7 \quad \Sigma x ^ { 2 } = 0.2312$$
  1. Calculate unbiased estimates of the population mean and variance.
  2. Test, at the \(10 \%\) significance level, whether the mean level of pollutant has changed.