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.
130 exam-style questions on WJEC A Level Maths 4.3.2 Statistical hypothesis testing (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.