AQA Further Paper 3 Statistics 2021 June — Question 4

Exam BoardAQA
ModuleFurther Paper 3 Statistics (Further Paper 3 Statistics)
Year2021
SessionJune
TopicCentral limit theorem

4 Oscar is studying the daily maximum temperature in \({ } ^ { \circ } \mathrm { C }\) in a village during the month of June. He constructs a \(95 \%\) confidence interval of width \(0.8 ^ { \circ } \mathrm { C }\) using a random sample of 150 days. He assumes that the daily maximum temperature has a normal distribution.
4
  1. Find the standard deviation of Oscar's sample, giving your answer to three significant figures.
    4
  2. Oscar calculates the mean of his sample to be \(25.3 ^ { \circ } \mathrm { C }\)
    He claims that the population mean is \(26.0 ^ { \circ } \mathrm { C }\)
    Explain whether or not his confidence interval supports his claim.
    4
  3. Explain how Oscar could reduce the width of his 95\% confidence interval.