6 Certain types of food are now sold in metric units. A random sample of 1000 shoppers was asked whether they were in favour of the change to metric units or not. The results, classified according to age, were as shown in the table.
| \cline { 2 - 4 }
\multicolumn{1}{c|}{} | Age of shopper | |
| \cline { 2 - 4 }
\multicolumn{1}{c|}{} | Under 35 | 35 and over | Total |
| In favour of change | 187 | 161 | 348 |
| Not in favour of change | 283 | 369 | 652 |
| Total | 470 | 530 | 1000 |
- Use a \(\chi ^ { 2 }\) test to show that there is very strong evidence that shoppers' views about changing to metric units are not independent of their ages.
- The data may also be regarded as consisting of two random samples of shoppers; one sample consists of 470 shoppers aged under 35 , of whom 187 were in favour of change, and the second sample consists of 530 shoppers aged 35 or over, of whom 161 were in favour of change. Determine whether a test for equality of population proportions supports the conclusion in part (i).