6 Yusha investigates the proportion of left-handed people living in two cities, \(A\) and \(B\). He obtains data from random samples from the two cities. His results are shown in the table, in which \(L\) denotes "left-handed".
| \(L\) | \(L ^ { \prime }\) |
| \(A\) | 14 | 9 |
| \(B\) | 26 | 51 |
- Test at the 10\% significance level whether there is association between being left-handed and living in a particular city.
A person is chosen at random from one of the cities \(A\) and \(B\).
Let \(A\) denote "the person lives in city \(A\) ". - State the relationship between \(\mathrm { P } ( L )\) and \(P ( L \mid A )\) according to the model implied by the null hypothesis of your test.
- Use the data in the table to suggest a value for \(P ( L \mid A )\) given by an improved model.