A-level · Hypothesis testing

Hypothesis testing for zero correlationExam-style questions

Testing whether a population has any linear correlation by comparing the sample PMCC r against a critical value from tables — choosing one- or two-tailed hypotheses on ρ, and concluding in context.

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26 questions · A-level level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 3 Level 4 Level 5

1
A sample of $n = 10$ gives a PMCC of $r = 0.72$ . Test, at the $5\%$ significance level, whether there is positive correlation in the population. The critical value is $0.5494$ .
Level 3 · 3 marksTry it
2
A sample of $n = 12$ gives $r = -0.62$ . Test at the $5\%$ level whether there is correlation in the population. For this two-tailed test the critical value is $0.5760$ .
Level 3 · 3 marksTry it
3
A sample of $n = 10$ gives $r = 0.40$ . Test at the $5\%$ level whether there is positive correlation. The critical value is $0.5494$ .
Level 3 · 3 marksTry it
4
For $5$ pairs of data, $\sum x = 15$ , $\sum y = 20$ , $\sum xy = 69$ , $\sum x^2 = 55$ , $\sum y^2 = 90$ .
(a) Show that $r = 0.900$ .
(b) Test at the $5\%$ level for positive correlation. The critical value is $0.8054$ .
Level 3 · 5 marksTry it
5
A sample of $n = 15$ pairs gives a product moment correlation coefficient of $r = 0.52$ .

Test, at the $5\%$ significance level, whether there is evidence of positive correlation in the population. The critical value for $n = 15$ is $0.4409$ . (4 marks)
Level 3 · 4 marksTry it

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