Worksheets · Foundation and Higher

Samples, populations and statistical claims

3 exam-style questions. Answers and the mark for each step are on the last page.

Question 1Non-calculator · 2 marks
A head teacher wants to know how long the 900 students at her school spend on homework each week.
(a) Which sample is most likely to represent the whole school? (1)
1. All of one Year 7 class
2. 50 students picked at random from the whole school register
3. 50 students at the homework club
(b) Explain why the homework club sample would be biased. (1)
Question 2Non-calculator · 3 marks
A college has 240 students. A simple random sample of 30 students includes 9 who walk to college.
(a) Estimate the number of students at the college who walk. (2)
(b) Give one reason why your estimate may differ from the true number. (1)
Question 3Calculator · 4 marks
Two random samples are taken from the 18 000 adults in a town. In sample $A$ , 12 of 50 adults are left-handed. In sample $B$ , 30 of 150 adults are left-handed.
(a) Use both samples to work out the best estimate for the number of left-handed adults in the town. (3)
(b) Explain why your estimate is better than one from sample $A$ alone. (1)

Answers and marks

(a) 50 students picked at random from the whole school register

(b) Students at homework club are likely to spend more time on homework than other students.

C1 A reason linking the club members to more (or different) homework time than the whole school.

(a) $72$

(b) Random samples vary, so the sample proportion may differ from the population proportion even with an unbiased selection method.

C1 Correct conclusion with supporting reasoning: Random samples vary, so the sample proportion may differ from the population proportion even with an unbiased selection method.

(a) 3780

(b) It is based on 200 people rather than 50, so it is likely to be closer to the true proportion.

Samples, populations and statistical claims

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