A-LevelMathematicsProbability and statistics9709/61 · Oct/Nov 2020 · Q27 Marks

In a survey, a random sample of 250 adults in Fromleigh were asked to fill in a questionnaire about their travel.

(a)It was found that 102 adults in the sample travel by bus. Find an approximate 90% confidence interval for the proportion of all the adults in Fromleigh who travel by bus.[3]
(b)The survey included a question about the amount, x dollars, spent on travel per year. The results are summarised as follows. n = 250 Σx = 50460 Σx² = 19 854 200 Find unbiased estimates of the population mean and variance of the amount spent per year on travel.[3]
(c)A councillor wanted to select a random sample of houses in Fromleigh. He planned to select the first house on each of the 143 streets in Fromleigh. Explain why this would not provide a random sample.[1]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2020). The mark or mark type is shown in brackets.

[M1] Any z but must be a z value. One side of the interval scores M1.
[B1]
[A1] Must be an an interval.
[B1] Allow without units. Allow 3s.f. $202.
[M1]
[A1] Allow with missing units. (Calculation of biased gives 38 700 scores M0A0)
[B1] e.g. Every house doesn't have an equal chance of being selected or most houses have no chance of being selected. Or other similar e.g. Houses in streets with few houses are more likely to be selected. Not just ‘biased', OE, without explanation

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