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.
121 exam-style questions on OCR A Level Maths 2.2 Data Presentation and Interpretation, covering 2.2.1 Tables and diagrams for single variable data, 2.2.2 Area in a histogram, 2.2.3 Scatter diagrams and regression lines, 2.2.4 Informal interpretation of correlation, 2.2.5 Correlation and causation, 2.2.6 Measures of average and spread, 2.2.7 Calculations of mean and standard deviation, 2.2.8 Outliers, 2.2.9 Selecting or critiquing data presentation, and 2.2.10 Cleaning data. Each one has a worked solution and a mark scheme showing where the marks go.