CAIE Mathematics A2 6.4.8 Proportion confidence intervals

[Maximum number: 4]

A student wishes to estimate the proportion, p, of students at her college who have exactly one brother. She surveys a random sample of 50 students at her college and finds that 18 of them have exactly one brother. She calculates an approximate $\alpha \%$ confidence interval for p and finds that the lower limit of the confidence interval is 0.244 correct to 3 significant figures.

Find $\alpha$ correct to the nearest integer.

$\frac{18}{50}-z \times \sqrt{\frac{\frac{18}{50} \times\left(1-\frac{18}{50}\right)}{50}}=0.244$
Use of correct equation.

z=1.709 or 1.708
Marking guidance:

Accept 1.71 if nothing better seen.

$\phi^{-1}\left({ }^{\prime} 1.709^{\prime}\right)=0.956 ; 1-2\left(1-{ }^{\prime} 0.956^{\prime}\right)$

[= 0.912]
Attempt area above or below their 1.709 and use correct method to find $\alpha$ .

$\alpha=91$
Allow $\alpha=91 \%$

0.91 or 91.2 score A0.

CAIE A-Level Mathematics A2 6.4.8 Proportion Confidence Intervals Questions question 1