For a random sample of 15 farms, the sample correlation between annual rainfall and wheat yield is r=0.462r=0.462r=0.462. A researcher tests H0:ρ=0H_0:\rho=0H0:ρ=0 against H1:ρ>0H_1:\rho>0H1:ρ>0. The one-tailed p-value is 0.0410.
State the conclusion at the 5% significance level.
Another researcher uses a two-tailed test on the same data. The two-tailed p-value is 0.0820. State the conclusion and explain the difference.
Explain why a significant positive correlation would not prove that greater rainfall causes a higher wheat yield.
178 exam-style questions on WJEC A Level Maths 4.3.1 Statistical hypothesis testing (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.