A meteorologist recorded the average daily rainfall (RRR) and the number of umbrellas sold (UUU) at a local shop for 12 selected days.
| Rainfall (R R\,R mm) | 2.5 | 4.0 | 5.5 | 8.0 | 10.5 | 12.0 | 15.0 | 18.0 | 20.0 | 22.0 | 25.0 | 28.0 |
| Umbrellas sold (UUU) | 3 | 7 | 5 | 12 | 10 | 18 | 15 | 22 | 19 | 28 | 24 | 30 |
Draw a scatter graph for this information.
Give an interpretation of the correlation between rainfall and umbrellas sold.
The equation of the regression line is U=1.05R+1.22U = 1.05R + 1.22U=1.05R+1.22.
Give an interpretation of the gradient of this regression line.
The product moment correlation coefficient is calculated to be 0.55.
Stating your hypotheses clearly, test at the 5% significance level whether there is a positive correlation between rainfall and umbrella sales.
Determine whether you would reach the same conclusion at the 1% significance level.
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.