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Date May 2022 Marks available 1 Reference code 22M.1.SL.TZ2.8
Level Standard Level Paper Paper 1 Time zone Time zone 2
Command term State Question number 8 Adapted from N/A

Question

A study was conducted to investigate whether the mean reaction time of drivers who are talking on mobile phones is the same as the mean reaction time of drivers who are talking to passengers in the vehicle. Two independent groups were randomly selected for the study.

To gather data, each driver was put in a car simulator and asked to either talk on a mobile phone or talk to a passenger. Each driver was instructed to apply the brakes as soon as they saw a red light appear in front of the car. The reaction times of the drivers, in seconds, were recorded, as shown in the following table.

At the 10% level of significance, a t-test was used to compare the mean reaction times of the two groups. Each data set is assumed to be normally distributed, and the population variances are assumed to be the same.

Let μ1 and μ2 be the population means for the two groups. The null hypothesis for this test is H0:μ1μ2=0.

State the alternative hypothesis.

[1]
a.

Calculate the p-value for this test.

[2]
b.

State the conclusion of the test. Justify your answer.

[2]
c.i.

State what your conclusion means in context.

[1]
c.ii.

Markscheme

H1: μ1-μ20     μ1μ2        A1


Note:
Accept an equivalent statement in words, however reference to “population mean” must be explicit for A1 to be awarded.

 

[1 mark]

a.

0.0778   0.0778465        A2


Note:
Award A1 for an answer of 0.0815486 from not using a pooled estimate of the variance.

 

[2 marks]

b.

0.0778<0.1         R1

reject the null hypothesis         A1


Note:
Do not award R0A1.

 

[2 marks]

c.i.

there is (significant evidence of) a difference between the (population) mean reaction times        A1


Note:
Their conclusion in (c)(ii) must match their conclusion in (c)(i) to earn A1. Award A0 if their conclusion refers to mean reaction times in the sample.

 

[1 mark]

c.ii.

Examiners report

Candidates who attempted to write the alternative hypothesis symbolically were successful. Those who tried to write in words generally did not make it clear whether they were referring to “population mean” and hence, were unsuccessful.

a.

Several candidates gave the p-value from not using a pooled estimate of the variance. As stated in the Mathematics: application & interpretation guide to the syllabus, for the t-test, candidates should assume that the variance of the two groups is equal and therefore, the pooled two-sample t-test should be used.

b.

The justification and generic conclusion were well done. However, candidates struggled when attempting to write their conclusion in context, generally referring to the reaction times rather than the mean reaction times. The conclusions were often vague as to whether the candidates were referring to the population means or the sample means; hypothesis testing is a good example on where candidates need to work to improve the clarity of their writing.

c.i.
[N/A]
c.ii.

Syllabus sections

Topic 4—Statistics and probability » SL 4.11—Expected, observed, hypotheses, chi squared, gof, t-test
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Topic 4—Statistics and probability

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