Sarah owns an ice cream parlour. Over the course of 12 days in the summer, she records the number of hours of sunshine, hhh, and the volume of ice cream sold, V V\,V litres. The product moment correlation coefficient for these data is calculated as 0.72.
Stating your hypotheses clearly and using a 5% significance level, test whether there is a positive correlation between hours of sunshine and ice cream sales.
Sarah 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 Sarah's suggestion.
State, giving a reason, which variable would be the explanatory variable.
Sarah calculated the linear regression equation as V=15.5+4.2hV = 15.5 + 4.2hV=15.5+4.2h
Give an interpretation of the gradient of this regression equation.
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.