Standard +0.8 This question requires working backwards from a confidence interval bound to find the confidence level, involving manipulation of the standard CI formula for proportions and use of inverse normal tables. It's more challenging than routine CI construction as it requires algebraic rearrangement and understanding the relationship between z-values and confidence levels, but remains a standard S2-level problem with clear methodology once the approach is identified.
In a survey of 300 randomly chosen adults in Rickton, 134 said that they exercised regularly. This information was used to calculate an \(\alpha\)% confidence interval for the proportion of adults in Rickton who exercise regularly. The upper bound of the confidence interval was found to be 0.487, correct to 3 significant figures.
Find the value of \(\alpha\) correct to the nearest integer. [4]
In a survey of 300 randomly chosen adults in Rickton, 134 said that they exercised regularly. This information was used to calculate an $\alpha$% confidence interval for the proportion of adults in Rickton who exercise regularly. The upper bound of the confidence interval was found to be 0.487, correct to 3 significant figures.
Find the value of $\alpha$ correct to the nearest integer. [4]
\hfill \mbox{\textit{CAIE S2 2023 Q2 [4]}}