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.
616 exam-style questions on Edexcel A Level Maths The Normal Distribution, covering 3.1 The Normal Distribution, 3.2 Finding Probabilities for Normal Distributions, 3.3 The Inverse Normal Distribution Function, 3.4 The Standard Normal Distribution, 3.5 Finding the mean and standard deviation, 3.6 Approximating a Binomial Distribution, and 3.7 Hypothesis Testing with the Normal Distribution. Each one has a worked solution and a mark scheme showing where the marks go.