Mathematical Methods — Question 8

QCAA 2023, Paper 1 · 1 mark

Q8 · 2023 · Technology-freeSimple familiar1 mark

QUESTION 8

For a 95% confidence interval with margin of error

E=0.03

z=1.96

and estimated proportion

0.6

, which expression gives the required sample size?

(A)

\frac{0.6}{(0.03/1.96)^2}

(B)

\frac{0.24}{(0.03/1.96)^2}

(C)

\frac{0.4}{(0.03/1.96)^2}

(D)

\frac{0.24}{(1.96/0.03)^2}

ABCD

WORKED SOLUTION

1 mark

ANSWER

B —

\frac{0.24}{(0.03/1.96)^2}

Worked solution

E=z\sqrt{p(1-p)/n}

, so

n=p(1-p)/(E/z)^2=0.24/(0.03/1.96)^2

; B.

Selects option B.

[1 mark]

Worked explanation by QCE Vault; correct option verified against the QCAA answer key.