The OCR Large Data Set gives travel-to-work counts for local authorities in England and Wales in 2001 and 2011. A student selects six local authorities in the North East and calculates the percentage-point changes, from 2001 to 2011, in the proportions of employed people who worked mainly at or from home, hhh, and who travelled by train, ttt.
Local authority: Darlington, Gateshead, Newcastle upon Tyne, North Tyneside, South Tyneside, Stockton-on-Tees
hhh: 0.264, -0.011, 0.102, 0.055, -0.359, 0.140
ttt: 0.568, 0.096, 0.221, 0.209, -0.111, 0.674
Use your calculator to find the product moment correlation coefficient between h h\,h and ttt. Give your answer to 3 significant figures.
The student wants to test whether there is positive correlation in the population of local authorities. State suitable null and alternative hypotheses.
For a sample of size 6, the critical value for a one-tailed test at the 5% significance level is 0.7293. Carry out the test at the 5% significance level.
The student claims that an increase in working from home causes an increase in travelling by train. Comment on this claim and on the use of these six local authorities to represent all local authorities in England and Wales.