A sociologist is investigating whether there is any correlation between the number of hours a week a person spends commuting and that person's reported level of job satisfaction.
She takes a random sample of 40 people and obtains a product moment correlation coefficient of -0.345.
The table below gives the critical values of the product moment correlation coefficient for a sample of size 40.
Two-tailed significance level: 10%, 5%, 2%, 1%
Critical value: 0.2638, 0.3120, 0.3665, 0.4026
State suitable null and alternative hypotheses for the sociologist's test.
Carry out the hypothesis test at the 5% significance level.
Determine every significance level in the table at which the null hypothesis would be rejected, justifying your answer.
244 exam-style questions on AQA A Level Maths 2.2 L: Data presentation and interpretation, covering 2.2.1 Single-variable data diagrams, 2.2.2 Scatter diagrams and correlation, 2.2.3 Central tendency, variation and standard deviation, 2.2.4 Outliers and cleaning data, and 2.2 L: Data presentation and interpretation. Each one has a worked solution and a mark scheme showing where the marks go.