A study of 20 students compares the time spent studying (t t\,t hours) and their final test scores (s s\,s marks).
The product moment correlation coefficient for the sample is r=0.435r = 0.435r=0.435.
Stating your hypotheses clearly test, at the 2.5% significance level, whether there is a positive correlation between study time and test scores.
316 exam-style questions on OCR A Level Maths 2.5 Statistical Hypothesis Testing, covering 2.5.1 The language of hypothesis testing, 2.5.2 Hypothesis test for a binomial proportion, 2.5.3 Inference and significance level, 2.5.4 Sample mean as a random variable (A-level only), 2.5.5 Hypothesis test for the mean of a normal distribution (A-level only), 2.5.6 Pearson's product-moment correlation coefficient, and 2.5.7 Hypothesis test using Pearson's coefficient (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.