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Date	November 2019	Marks available	1	Reference code	19N.3.AHL.TZ0.Hsp_1
Level	Additional Higher Level	Paper	Paper 3	Time zone	Time zone 0
Command term	State	Question number	Hsp_1	Adapted from	N/A

Question

Peter, the Principal of a college, believes that there is an association between the score in a Mathematics test, $X$ , and the time taken to run 500 m, $Y$ seconds, of his students. The following paired data are collected.

It can be assumed that $\left( {X{\text{, }}Y} \right)$ follow a bivariate normal distribution with product moment correlation coefficient $\rho$ .

State suitable hypotheses ${H_0}$ and ${H_1}$ to test Peter’s claim, using a two-tailed test.

[1]

a.i.

Carry out a suitable test at the 5 % significance level. With reference to the $p$ -value, state your conclusion in the context of Peter’s claim.

[4]

a.ii.

Peter uses the regression line of $y$ on $x$ as $y = 0.248x + 83.0$ and calculates that a student with a Mathematics test score of 73 will have a running time of 101 seconds. Comment on the validity of his calculation.

[2]

b.

Markscheme

${H_0}\,{\text{:}}\,\rho = 0$ ${H_1}\,{\text{:}}\,\rho \ne 0$ A1

Note: It must be $\rho$ .

[1 mark]

a.i.

$p = 0.649$ A2

Note: Accept anything that rounds to 0.65

0.649 > 0.05 R1

hence, we accept ${H_0}$ and conclude that Peter’s claim is wrong A1

Note: The A mark depends on the R mark and the answer must be given in context. Follow through the $p$ -value in part (b).

[4 marks]

a.ii.

a statement along along the lines of ‘(we have accepted that) the two variables are independent’ or ‘the two variables are weakly correlated’ R1

a statement along the lines of ‘the use of the regression line is invalid’ or ‘it would give an inaccurate result’ R1

Note: Award the second R1 only if the first R1 is awarded.

Note: FT the conclusion in(a)(ii). If a candidate concludes that the claim is correct, mark as follows: (as we have accepted H₁) the 2 variables are dependent and 73 lies in the range of $x$ values R1, hence the use of the regression line is valid R1.

[2 marks]

b.

Examiners report

[N/A]

a.i.

[N/A]

a.ii.

[N/A]

b.

Syllabus sections

Topic 4—Statistics and probability » SL 4.4—Pearsons, scatter diagrams, eqn of y on x

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Find Pearson’s product-moment correlation coefficient, $r$ , for these data.
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Find Pearson’s product-moment correlation coefficient, $r$ , for these data.
21N.2.AHL.TZ0.1e:
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State how, if at all, the value of $r$ would be affected.
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Find the percentage error in your estimate in part (d).
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State whether it is valid to use the regression line to estimate the average weight of the brain of mice. Give a reason for your answer.
18N.2.SL.TZ0.T_1c.ii:
Justify whether it is valid to use the regression line y on x to estimate Jerome’s examination score.
18N.2.SL.TZ0.T_1d:
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Calculate the percentage error in Jerome’s estimated examination score.
16N.2.SL.TZ0.T_1a:
On graph paper, draw a scatter diagram for these data. Use a scale of 2 cm to represent 5 hours on the $x$ -axis and 2 cm to represent 10 points on the $y$ -axis.
16N.2.SL.TZ0.T_1b:
(i) ${\bar x}$ , the mean number of hours spent on social media;

(ii) ${\bar y}$ , the mean number of IB Diploma points.
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Draw the regression line, from part (e), on your scatter diagram.
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Use the given equation of the regression line to estimate the number of IB Diploma points that this girl obtained.
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Label the point ${\text{M}}(\bar x,{\text{ }}\bar C)$ on the scatter diagram.
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State a reason why the regression line $C$ on $x$ is appropriate to model the relationship between these variables.
17M.2.SL.TZ2.T_3g:
Draw the regression line $C$ on $x$ on the scatter diagram.
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Use the equation of the regression line to estimate the least number of folders that the factory needs to sell in a month to exceed its production cost for that month.

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