Mathematics 9709 · AS & A Level · Sampling and estimation
Sampling and estimation — practice question
Henri is intending to take a random sample of 804 students at his college. He labels the students from 1 to 804 and then applies random numbers from his calculator. The first 20 random digits produced by his calculator are these: 5 6 7 1 0 9 8 4 3 1 0 9 6 6 5 0 2 1 7 6. Henri’s first two student numbers are 567 and 109.
The sample contained 30 students. He asked each student to state how many hours, $X$, they spent on social media each week, on average. He presented the results as follows: $n = 30$, $\Sigma x = 610$, $\Sigma x^2 = 12405$.
(a)[2]
Use Henri’s digits to work out the numbers of the next two students in the sample.
(b)[3]
Use the information given to calculate an unbiased estimate of the mean of $X$ and show that an unbiased estimate of the variance of $X$ is less than $0.1$.
(c)[1]
Henri’s friend says that Henri has probably made a mistake in his calculation of $\Sigma x$ or $\Sigma x^2$. Use your answer to part (b) to comment on this claim.
Worked solution & mark scheme
This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: “State two correct values from $567, 109, 665, 21$ (allow $021$), $\,$ B1 for each.” …