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.
355 exam-style questions on OCR (MEI) A Level Maths 2.5 Statistical Hypothesis Testing, covering 2.5.1 Process and language of hypothesis testing, 2.5.2 When to apply 1-tail and 2-tail tests, 2.5.3 Significance level and incorrect rejection, 2.5.4 Null and alternative hypotheses (binomial), 2.5.5 Conduct a binomial hypothesis test, 2.5.6 Critical and acceptance regions (binomial), 2.5.7 Distribution of the sample mean (A-level only), 2.5.8 Hypothesis test for a single mean (A-level only), 2.5.9 Critical and acceptance regions (mean) (A-level only), 2.5.10 Correlation as closeness to a straight line (A-level only), 2.5.11 Inference using a correlation coefficient (A-level only), and 2.5 Statistical Hypothesis Testing. Each one has a worked solution and a mark scheme showing where the marks go.