Mathematical Methods — Question 12

QCAA 2025, Paper 1 · 4 marks

Q12 · 2025 · Technology-freeSimple familiar4 marks

QUESTION 12 (4 marks)

A teacher conducted a survey about student involvement in school activity groups. They found that of a random sample of 25 students, five students were members of the environment group. Determine the approximate confidence interval for the proportion of students at the school who are members of the environment group, using

z=1

. Express your answer using fractions in simplified form.

Question linkOriginal paper

WORKED SOLUTION

QCAA guide · typeset solution

4 marks

ANSWER

(\frac3{25},\frac7{25})

Worked solution

n=25

and

\hat p=\frac5{25}=\frac15.

Using

\hat p\pm z\sqrt{\frac{\hat p(1-\hat p)}{n}},

with

z=1

gives a margin of error

\sqrt{\frac{(1/5)(4/5)}{25}}=\frac2{25}.

Therefore the confidence interval is

\left(\frac5{25}-\frac2{25},\frac5{25}+\frac2{25}\right)=\left(\frac3{25},\frac7{25}\right).

correctly determines the sample proportion

[1 mark]

substitutes the sample size, sample proportion and z-value into at least one end of approximate confidence interval formula

[1 mark]

determines the approximate margin of error

[1 mark]

determines the lower and upper end of the approximate confidence interval

[1 mark]

One QCAA sample method typeset for web; criterion wording is adapted from the official marking guide.

View the full QCAA marking guide

How many marks did you earn?

Compare your working with the guide above.

Mathematical Methods — Question 12

QUESTION 12 (4 marks)

QCAA guide · typeset solution

Related questions