Solved: The Malvern Aquatic Center hosted a 3 metre spring board diving event. The... [IB Mathematics Applications & Interpretation (Math AI)]

Question

SLPaper 2

The Malvern Aquatic Center hosted a 3 metre spring board diving event. The judges, Stan andMinsun awarded 8 competitors a score out of 10. The raw data is collated in the following table.

The Commissioner for the event would like to find the Spearman’s rank correlation coefficient.

Write down the value of the Pearson’s product–moment correlation coefficient, $r$ .

[2]

Verified

Solution

0.909 (0.909181…) A2

[2 marks]

Using the value of $r$ , interpret the relationship between Stan’s score andMinsun’s score.

[2]

Verified

Solution

(very) strong and positive A1A1

Note: Award A1 for (very) strong A1 for positive.

[2 marks]

Write down the equation of the regression line $y$ on $x$ .

[2]

Verified

Solution

$y = 1.14x + 0.578\,\,\left( {y = 1.14033 \ldots x + 0.578183 \ldots } \right)$ A1A1

Note: Award A1 for $1.14x$ , A1 for $0.578$ . Award a maximum of A1A0if the answer is not an equation in the form $y = mx + c$ .

[2 marks]

Use your regression equation from part (b) to estimate Minsun’s score when Stanawards a perfect 10.

[2]

Verified

Solution

1.14 × 10+ 0.578 M1

12.0 (11.9814…) A1

[2 marks]

State whether this estimate is reliable. Justify your answer.

[2]

Verified

Solution

no the estimate is not reliable A1

outside the known data range R1
OR
a score greater than 10 is not possible R1

Note: Do not award A1R0.

[2 marks]

Copy and complete the information in the following table.

[2]

Verified

Solution

A1A1

Note: Award A1 for correct ranks for Stan. Award A1 for correct ranks for Minsun.

[2 marks]

Find the value of the Spearman’s rank correlation coefficient, ${r_s}$ .

[2]

Verified

Solution

0.933 (0.932673…) A2

[2 marks]

Comment on the result obtained for ${r_s}$ .

[2]

Verified

Solution

Stan and Minsun strongly agree on the ranking of competitors. A1A1

Note: Award A1 for “strongly agree”, A1 for reference to a rank order.

[2 marks]

The Commissioner believes Minsun’s score for competitor G is too high and so decreasesthe score from 9.5 to 9.1.

Explain why the value of the Spearman’s rank correlation coefficient ${r_s}$ does not change.

[1]

Verified

Solution

decreasing the score to 9.1, does not change the rank of competitor G A1

[1 mark]

The Malvern Aquatic Center hosted a 3 metre spring board diving event. The judges, Stan andMinsun awarded 8 competitors a score out of 10. The raw data is collated in the following table.The Commissioner for the event would like to find the Spearman’s rank correlation coefficient.

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