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Edexcel IAL Mathematics S3.5.2 hypothesis tests for zero correlation

Practise correlation tests by setting hypotheses for zero correlation, choosing the right critical value and concluding from r or rs.

Syllabus
First assessment 2019
Course
Mathematics YMA01
Level
A2

Exam points

  • State H0: ρ=0 and choose one- or two-tailed H1 from wording such as positive correlation.
  • Compare r or rs with the critical value at the stated significance level.
  • Conclude in context whether the data support positive, negative or any correlation.

S3.5.2 - Hypothesis tests for zero correlation question 1

[Maximum number: 6]

The table shows the season's best times, x seconds, for the 8 athletes who took part in the 200 m final in the 2021 Tokyo Olympics. It also shows their finishing position in the race.

Table for Question S3.5.2 - Hypothesis tests for zero correlation question 1 — Edexcel A-Level Mathematics A2

Given that the fastest season's best time is ranked number 1

Question (a)

(a)

Stating your hypotheses clearly, test, at the 1% level of significance, whether or not there is evidence of a positive correlation between the rank of the season's best time and the finishing position for these athletes.

Chris suggests that it would be better to use the actual finishing time, y seconds, of these athletes rather than their finishing position.

Given that

Sxx=0.1286875Syy=0.55275Sxy=0.225175S_{x x}=0.1286875 \quad S_{y y}=0.55275 \quad S_{x y}=0.225175
[ 4 ]

Question (b)

(b)

Use your value of the product moment correlation coefficient to test, at the 1% level of significance, whether or not there is evidence of a positive correlation between the season's best time and the finishing time for these athletes.

[ 2 ]
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