A teacher records weekly independent-study time h h\,h hours and test score s s\,s for 10 students.
hhh: 1, 2, 2, 3, 4, 4, 5, 6, 7, 8 sss: 48, 52, 55, 57, 62, 65, 68, 74, 78, 85
Draw a scatter diagram and describe the association. The regression line is s=42.7+5.17hs=42.7+5.17hs=42.7+5.17h.
Interpret the gradient. The correlation coefficient is 0.995, with an associated one-tailed p-value less than 0.001.
Test for positive association at the 1% significance level, stating suitable hypotheses.
A further point, (8,45)(8,45)(8,45), is added. State and justify its likely effect on the correlation coefficient.
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.