Mathematics 9709 · AS & A Level · Sampling and estimation

Sampling and estimation — practice question

In a survey, a random sample of 250 adults in Fromleigh completed a questionnaire on their travel.
(a)[3]

The survey showed that 102 adults in the sample travel by bus. Calculate an approximate $90\%$ confidence interval for the proportion of all adults in Fromleigh who travel by bus.

(b)[3]

The survey asked about the yearly amount, $x$ dollars, spent on travel. The summary is $n = 250$, $\sum x = 50\,460$, $\sum x^2 = 19\,854\,200$. Find unbiased estimates of the population mean and the variance of the amount spent on travel per year.

(c)[1]

A councillor wanted to draw a random sample of houses in Fromleigh. He intended to choose the first house on each of the 143 streets in Fromleigh. Explain why this would not produce a random sample.

Worked solution & mark scheme

This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: Write the confidence interval as $\frac{102}{250} \pm z\sqrt{\frac{0.000966144}{}}$ or another equivalent correct $z$-based form.

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