Standard +0.3 This is a straightforward confidence interval problem requiring students to work backwards from the interval width to find the confidence level. It involves standard formulas for proportions (width = 2z√(p̂(1-p̂)/n)) and looking up or calculating the z-value, but requires no conceptual insight beyond routine manipulation of the confidence interval formula. Slightly easier than average as it's a direct application with clear numerical values provided.
3 A researcher wishes to estimate the proportion, \(p\), of houses in London Road that have only one occupant. He takes a random sample of 64 houses in London Road and finds that 8 houses in the sample have only one occupant. Using this sample, he calculates that an approximate \(\alpha \%\) confidence interval for \(p\) has width 0.130 . Find \(\alpha\) correct to the nearest integer.
3 A researcher wishes to estimate the proportion, $p$, of houses in London Road that have only one occupant. He takes a random sample of 64 houses in London Road and finds that 8 houses in the sample have only one occupant. Using this sample, he calculates that an approximate $\alpha \%$ confidence interval for $p$ has width 0.130 . Find $\alpha$ correct to the nearest integer.\\
\hfill \mbox{\textit{CAIE S2 2018 Q3 [5]}}