An agricultural scientist measures the amount of fertilizer applied, f f\,f kg per hectare, and the resulting wheat yield, Y Y\,Y tonnes, for 15 experimental plots. The product moment correlation coefficient for these data is 0.61.
Stating your hypotheses clearly and using a 5% significance level, test whether there is a positive correlation between fertilizer amount and wheat yield.
The scientist suggests that a linear regression model could be used to model the data.
State, giving a reason, whether or not the correlation coefficient is consistent with the scientist's suggestion.
State, giving a reason, which variable would be the explanatory variable.
The scientist calculated the linear regression equation as Y=4.1+0.05fY = 4.1 + 0.05fY=4.1+0.05f
Give an interpretation of the gradient of this regression equation.
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.