Mathematical Methods — Question 17

QCAA 2020, Paper 2 · 4 marks

Q17 · 2020 · Technology-activeComplex familiar4 marks

QUESTION 17 (4 marks)

In a survey of 326 lecturers, 303 said that on at least one occasion a mobile phone had rung in a lecture they were giving. Determine the sample size required to conduct a follow-up survey that provides 95% confidence that this one-point estimate is correct to within

\pm0.02

of the population proportion.

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WORKED SOLUTION

QCAA guide · typeset solution

4 marks

ANSWER

630 lecturers

Worked solution

The sample proportion is

\hat p=303/326

. Using the 95% confidence-interval margin of error,

0.02=1.96\sqrt{\frac{(303/326)(23/326)}{n}}.

Solving gives

n=629.778

, so a sample of 630 lecturers is required.

correctly determines the sample proportion

[1 mark]

establishes equation in

n

[1 mark]

determines

n

[1 mark]

determines reasonable value of

n

[1 mark]

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Mathematical Methods — Question 17

QUESTION 17 (4 marks)

QCAA guide · typeset solution

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