A teacher recorded the number of hours spent revising and the resulting test scores for 12 students in a mathematics class. The data is presented in the table below.
| Revision Hours (hhh) | 2 | 4 | 5 | 7 | 8 | 10 | 12 | 14 | 15 | 17 | 18 | 20 |
| Test Score (sss) | 45 | 50 | 48 | 60 | 65 | 70 | 72 | 80 | 85 | 88 | 92 | 95 |
Draw a scatter graph for this information.
Give an interpretation of the correlation between the number of hours spent revising and the test scores.
The equation of the regression line for this data is s=2.95h+38.4s = 2.95h + 38.4s=2.95h+38.4.
Give an interpretation of the gradient of this regression line.
The product moment correlation coefficient (PMCC) for this data is calculated to be 0.992.
Stating your hypotheses clearly, test at the 5% significance level whether there is a positive correlation between revision hours and test scores.
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.