DP Mathematics: Applications and Interpretation Questionbank

Hence comment on the validity of the written assessment as a measure of the level of performance of employees in this department. Justify your answer.

Without calculation, explain why it might not be appropriate to calculate a correlation coefficient for the whole sample of $18$ employees.

Find $r_s$ for the seven employees working in the international department.

Which of the correlation coefficients would you recommend is used to assess whether or not there is an association between total number of minutes late and distance from school? Fully justify your answer.

Find the value of the ${\chi }^2$ test statistic $\left({\chi }_{calc}^2\right)$ for this test.

Determine the degrees of freedom for Dana’s test.

It is given that the critical value for this test is $9.49$.

State the conclusion of the test in context. Use your answer to part (c) to justify your conclusion.

Copy and complete the information in the following table.

Calculate the value of $r_s$.

Interpret your result.

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

$b$.

$a$.

Interpret the value obtained for $r_s$.

$c$.

When calculating the ranks, Chester incorrectly read the Netherlands’ score as $478$. Explain why the value of the Spearman’s rank correlation $r_s$ does not change despite this error.

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

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

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

Comment on the result obtained for $r_s$.

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

State whether this estimate is reliable. Justify your answer.

Copy and complete the information in the following table.

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

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

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

Explain why it is not appropriate to use Pearson’s product moment correlation coefficient to measure the strength of the relationship between $P$ and $d$.

Calculate Spearman’s rank correlation coefficient for this data.

State what conclusion Charles can make from the answer in part (c).

Explain why it is appropriate to use Spearman’s rank correlation coefficient to measure the strength of the relationship between $P$ and $d$.

Calculate Spearman’s rank correlation coefficient for this data.

State what conclusion Kayla can make from the answer in part (a).