An agricultural scientist observed that the product moment correlation coefficient between the amount of rainfall (in mm) and the yield of a specific crop (in tonnes per hectare) for a sample of 30 farms was 0.412. The data is assumed to come from a bivariate normal distribution. Carry out a hypothesis test at the 5% significance level to determine whether there is a positive correlation between rainfall and crop yield. The critical value for the correlation coefficient at the 5% significance level for a sample size of 30 is 0.3061.
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.