This document contains exam done on May 2022 OCR AS Level Further Mathematics A Y532/01 Statistics. Question Paper. Download to score an A.

Answer all the questions.

1 A geography student chose a certain point in a stream and took measurements of the speed of

flow, vms-1

, of water at various depths, dm, below the surface at that point. The results are

shown in the table.

d 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

v 0.8 0.5 0.7 1.2 1.1 1.3 1.6 1.4 0.4

n = 9 /d = 2.7 /v = 9.0 d2 / = 0.96 v

2 / = 10.4 /dv = 2.85

(a) (i) Explain why d is an example of an independent, controlled variable. [1]

 (ii) Use two relevant terms to describe the variable v in a similar way. [1]

A statistician believes that the point (0.5, 0.4) may be an anomaly.

(b) Calculate the equation of the least squares regression line of v on d for all the points in the

table apart from (0.5, 0.4). [2]

(c) Use the equation of the line found in part (b) to estimate the value of v when d = 0.5. [1]

(d) Use your answer to part (c) to comment on the statistician’s belief. [1]

(e) Use the diagram in the Printed Answer Booklet (which does not illustrate the data in this

question) to explain what is meant by “least squares regression line”. [2]

2 Eight runners took part in two races. The positions in which the runners finished in the two races

are shown in the table.

Runner A B C D E F G H

First race 3 1 5 6 2 8 7 4

Second race 4 3 8 7 2 5 6 1

Test at the 5% significance level whether those runners who do better in one race tend to do better

in the other. [7]

3 A discrete random variable X has the following probability distribution.

x 1 2 3 4

P(X = x) p 0.31 0.3 p

2

(a) Determine the value of p. [3]

(b) It is given that E(aX + b) = Var(aX + b) = 23.19, where a and b are positive constants.

Determine the value of a and the value of b