Q11 · 2023 · Technology-activeSimple familiar4 marks
QUESTION 11 (4 marks)
A researcher found that 17 out of 50 randomly selected people had used public transport in the past week.
a)[1 mark]
Determine the sample proportion of people who had used public transport in the past week.
b)[2 marks]
Determine an approximate 95% confidence interval for the proportion of people who had used public transport in the past week.
c)[1 mark]
Someone claims that: **50% of people use public transport each week.** Use your answer from Question 11b) to explain whether the data can or cannot support this claim.
WORKED SOLUTION
4 marksQCAA guide · typeset solution
ANSWER
a) ; b) ; c) the claim is not supported.
Worked solution
a)
b) Using the formula to estimate variance, so the standard deviation is . Using GDC InvN with area , standard deviation and ,
c) From Question 11b), we are 95% confident that the proportion of people using public transport is approximately between 21% and 47%. 50% is outside of this range. The claim is not supported.
correctly determines the sample proportion
identifies all the information required to establish the confidence interval
determines an approximate 95% confidence interval
provides a valid evaluation of the claim that references their answer from 11b)
One QCAA sample method typeset for web; criterion wording is adapted from the official marking guide.
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