6 Random samples of 200 'Alpha' and 150 'Beta' vacuum cleaners were monitored for reliability. It was found that 62 Alpha and 35 Beta cleaners required repair during the guarantee period of one year. The proportions of all Alpha and Beta cleaners that require repair during the guarantee period are \(p _ { \alpha }\) and \(p _ { \beta }\) respectively.

1. Find a \(95 \%\) confidence interval for \(p _ { \alpha }\).
2. Give a reason why, apart from rounding, the interval is approximate.
3. Test, at the \(5 \%\) significance level, whether \(p _ { \alpha }\) differs from \(p _ { \beta }\).