Edexcel S4 2017 June — Question 1

Exam BoardEdexcel
ModuleS4 (Statistics 4)
Year2017
SessionJune
TopicLinear combinations of normal random variables
TypeTwo-sample t-test (unknown variances)
  1. The times taken by children to run 150 m are normally distributed. The times taken, \(x\) seconds, by a random sample of 9 boys and an independent random sample of 6 girls are recorded. The following statistics are obtained.
Number of childrenSample mean \(\bar { x }\)\(\sum x ^ { 2 }\)
Boys922.84693.60
Girls629.55236.12
  1. Test, at the \(10 \%\) level of significance, whether or not the variances of the two distributions are equal. State your hypotheses clearly. The Headteacher claims that the mean time taken for the girls is more than 5 seconds greater than the mean time taken for the boys.
  2. Stating your hypotheses clearly, test the Headteacher's claim. Use a \(1 \%\) level of significance and show your working clearly.
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