CAIE S2 2020 November — Question 2

Exam BoardCAIE
ModuleS2 (Statistics 2)
Year2020
SessionNovember
TopicHypothesis test of a normal distribution

2 In a survey, a random sample of 250 adults in Fromleigh were asked to fill in a questionnaire about their travel.
  1. It was found that 102 adults in the sample travel by bus. Find an approximate \(90 \%\) confidence interval for the proportion of all the adults in Fromleigh who travel by bus.
  2. The survey included a question about the amount, \(x\) dollars, spent on travel per year. The results are summarised as follows. $$n = 250 \quad \Sigma x = 50460 \quad \Sigma x ^ { 2 } = 19854200$$ Find unbiased estimates of the population mean and variance of the amount spent per year on travel.
    A councillor wanted to select a random sample of houses in Fromleigh. He planned to select the first house on each of the 143 streets in Fromleigh.
  3. Explain why this would not provide a random sample.