An educational psychologist believes that students who attend after-school tutoring sessions achieve a mean test score that is more than 8 points higher than students who study independently.
A random sample of 75 students who attend tutoring sessions had a mean score of 76.4 with a standard deviation of 9.2.
A random sample of 90 students who study independently had a mean score of 65.2 with a standard deviation of 11.5.
Stating your hypotheses clearly, test the psychologist's claim at the 5% level of significance.
State whether it was necessary to assume that the test scores of students are normally distributed. Give a reason for your answer.
162 exam-style questions on AQA A Level Maths 2.5 O: Statistical hypothesis testing, covering 2.5.1 Language of hypothesis testing, 2.5.2 Hypothesis test for a binomial proportion, and 2.5.3 Hypothesis test for a Normal mean (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.