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.
209 exam-style questions on CCEA A Level Maths 4.6 Statistical hypothesis testing (A-level only), covering 4.6.1 Statistical hypothesis testing (A-level only), 4.6.2 Statistical hypothesis testing (A-level only), 4.6.3 Statistical hypothesis testing (A-level only), 4.6.4 Statistical hypothesis testing (A-level only), and 4.6.5 Statistical hypothesis testing (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.