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.

Start practising Read the lesson

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 $r = -0.55$ . Test at the $5\%$ level whether there is negative correlation in the population. The critical value is $0.5494$ .
Level 4 · 3 marksTry it
2
For $8$ pairs of data the PMCC is found to be $r = 0.956$ . Test at the $5\%$ level whether there is correlation in the population. For this two-tailed test with $n = 8$ the critical value is $0.7067$ .
Level 4 · 3 marksTry it
3
A sample of $n = 20$ gives $r = 0.45$ . Test at the $5\%$ level whether there is positive correlation. The critical value is $0.3783$ .
Level 4 · 3 marksTry it
4
A sample of $n = 12$ pairs gives $r = -0.61$ .

Test, at the $5\%$ significance level, whether there is evidence of ANY correlation (positive or negative). The two-tail critical value for $n = 12$ is $0.5760$ . (4 marks)
Level 4 · 4 marksTry it
5
A researcher records the number of hours of revision, $x$ , and the test score, $y$ , for a random sample of $20$ students. The product moment correlation coefficient for the sample is $r = 0.561$ .
(a) State what is measured by the product moment correlation coefficient. (1 mark)
(b) Test, at the $1\%$ level of significance, whether there is positive correlation between hours of revision and test score.

The critical value of $r$ for a one-tailed test at the $1\%$ level with $n = 20$ is $0.5368$ . (5 marks)
(c) A second researcher analyses the same data but measures the revision time in minutes rather than hours. State, with a reason, the effect this has on the value of $r$ . (2 marks)
(d) Explain why this result does not show that revision causes higher test scores. (2 marks)

The equation of the regression line of $y$ on $x$ for this sample is $y = 31.2 + 2.4x$ .
(e) Use the regression line to estimate the test score of a student who revises for $8$ hours, and state one assumption needed for this estimate to be reliable. (2 marks)
Level 4 · 12 marksTry it

3 more questions on hypothesis testing for zero correlation

Free with an account — just an email, no card. The whole bank, every mark scheme and worked solution.

Start free