DP Mathematics: Applications and Interpretation Questionbank

Calculate the mean annual income for these remaining responses.

Determine the value of $r$, Pearson’s product-moment correlation coefficient, for these remaining responses.

Use Juliet’s data to find the value of $a$ and of $b$.

Interpret, referring to income and happiness, what the value of $a$ represents.

Find the value of $a$ and of $b$.

Write down the correlation coefficient.

Using the regression equation, estimate the number of hot chocolates that Lucy will sell on a day when the maximum temperature is $12°\text{C}$.

On graph paper, draw a scatter diagram to show the results of Don’s investigation. Use a scale of $1 \text{cm}$ to represent $2$ units on the $x$-axis, and $1 \text{cm}$ to represent $5$ units on the $y$-axis.

Calculate $\overline{x}$, the mean wind speed.

Calculate $\overline{y}$, the mean time to fully charge the robot.

Plot and label the point $\text{M}$ on your scatter diagram.

Calculate $r$, Pearson’s product–moment correlation coefficient.

Describe the correlation between the wind speed and the time to fully charge the robot.

Write down the equation of the regression line $y$ on $x$, in the form $y=mx+c$.

Draw this regression line on your scatter diagram.

Hence or otherwise estimate the charging time when the wind speed is $27 {\text{km\hspace{0.05em}h}}^{-1}$.

Don concluded from his investigation: “There is no causation between wind speed and the time to fully charge the robot”.

In the context of the question, briefly explain the meaning of “no causation”.

Assuming the data follows a linear model for this period, find the regression line of $T$ on $m$ for the remaining data.

State a more appropriate model for the water temperature in the lake over an extended period of time. You are not expected to calculate any parameters.

Explain why your line should not be used to estimate the value of $m$ at which the temperature is $10.0$ $°\mathrm{C}$.

Use your line to find an estimate for the water temperature on the first day of May.

Explain in context why your line should not be used to predict the value for December (month $12$).

Use your answer to part (b) to write down the value of $n$ to the nearest integer.

Find the equation of the least squares regression line of ${\log }_{10} P$ against ${\log }_{10} d$.

Find an expression for $P$ in terms of $d$.

Explain why this graph indicates that $P$ is inversely proportional to $d^n$.

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.

State whether it is valid to use the regression line $y$ on $x$ for Jason’s estimate. Give a reason for your answer.

Describe the correlation.

Find the percentage score calculated by Jason.

For this data, find the value of the Pearson’s product-moment correlation coefficient, $r$.

A 57-year-old male also ran in the $5000 \text{m}$ race.

Use the equation of the regression line to estimate the time he took to complete the $5000 \text{m}$ race.

Comment on your answer to part (a), using the information that Eduardo found.

Write down the equation of the regression line of $t$ on $x$, in the form $t=ax+b$.

Use the data in the second table to find the value of $m$ and the value of $b$ for the regression line, $\ln x=m(\ln d)+b$.

Assuming that the model found in part (a) remains valid, estimate the percentage of trees in stock when $d=25$.

Find the equation of the regression line of $h$ on $t$.

Suggest why Eva’s use of the linear regression equation in this way could be unreliable.

Find the equation of the least squares quadratic regression curve.

Find the value of $k$.

Hence, write down a suitable domain for Eva’s function $h\left(t\right)=p{t}^2+qt+r$.

Interpret the meaning of parameter $a$ in the context of the model.

By solving the differential equation $\frac{dh}{dt}=-R^2\sqrt{70 560h}$, show that the general solution is given by $h=17 640{\left(c-R^{2}t\right)}^2$, where $c\in \mathrm{ℝ}$.

Show that $\frac{dH}{dt}\approx 0.2514-0.009873t-0.1405\sqrt{H}$, where $0\le t\le T$.

Use Euler’s method with a step length of $0.5$ minutes to estimate the maximum value of $H$.

Use the general solution from part (d) and the initial condition $h\left(0\right)=3.2$ to predict the value of $T$.

Find this new height.

Show that $\frac{dh}{dt}=-R^2\sqrt{70 560h}$.

State whether it would be appropriate for Chester to use the equation of a regression line for $y$ on $x$ to predict a country’s Eurovision score. Justify your answer.

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.

find the value of $a$ and of $b$.

Find the equation of the regression line of $\text{ln}\left(T-25\right)$ on $t$.

Show that $\text{ln}\left(T-25\right)=bt+\text{ln}a$.

predict the temperature of the metal rod after 3 minutes.

$c$.

It is not required to state units for this value.

$A$.

It is not required to state units for this value.

Find the equation of the regression line of $Q\left(t\right)$ on $t$.

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

Use linear regression to estimate the value of $k$ and of $L$.

Find the probability that a fish from this lake will have a weight of more than 560 grams.

The maximum weight a hand net can hold is 6 kg. Find the probability that a catch of 11 fish can be carried in the hand net.

State the distribution of your test statistic, including the parameter.

Find the p-value for the test.

State the conclusion of the test, justifying your answer.

State suitable hypotheses for the test.

Find the product-moment correlation coefficient $r$.

State the p-value and interpret it in this context.

Use an appropriate regression line to estimate the weight of a fish with length 360 mm.

Find the value of a and of b.

Use the regression equation to estimate the value of y when x = 3.57.

The relationship between x and y can be modelled using the formula y = kxⁿ, where k ≠ 0 , n ≠ 0 , n ≠ 1.

By expressing ln y in terms of ln x, find the value of n and of k.

Find the value of a and of b.

Write down the correlation coefficient.

Use your equation to estimate the mean weight of a child that is 1.95 years old.

Write down the value of $a$ and of $b$.

Use this regression line to estimate the monthly honey production from a hive that has 270 bees.

Write down the number of low production hives.

Find the value of $k$;

Find the number of hives that have a high production.

Adam decides to increase the number of bees in each low production hive. Research suggests that there is a probability of 0.75 that a low production hive becomes a regular production hive. Calculate the probability that 30 low production hives become regular production hives.

Find the value of $a$ and of $b$.

Write down the value of  $r$.

Use the regression equation to estimate the number of visitors on a day when the maximum temperature is 15 °C.

Write down the independent variable.

Write down the boiling temperature of the liquid.

Jim describes the correlation as very strong. Circle the value below which best represents the correlation coefficient.

$$0.9920.2510-0.251-0.992$$

Jim’s model is $d=-2.24t+105$, for $0⩽t⩽20$. Use his model to predict the decrease in temperature for any 2 minute interval.

Another athlete on this sports team has a hand length of 21.5 cm. Use the regression equation to estimate the height of this athlete.

Write down the value of $a$ and of $b$.

Find the correlation coefficient.

Use the regression equation to estimate the BMI of an adult man whose waist size is 95 cm.

For these data, find Pearson’s product-moment correlation coefficient, r.

For these data, find the equation of the regression line y on x.

Using the equation of the regression line, estimate the concentration of dissolved oxygen in the river when the temperature is 18 °C.

Find the range of the average body weights for these seven species of mammal.

For the data from these seven species calculate $r$, the Pearson’s product–moment correlation coefficient;

For the data from these seven species describe the correlation between the average body weight and the average weight of the brain.

Write down the equation of the regression line $y$ on $x$, in the form $y=mx+c$.

Use your regression line to estimate the average weight of the brain of grey wolves.

Find the percentage error in your estimate in part (d).

Find the mean number of hours that the people surveyed watch television per week.

Draw the regression line on the scatter diagram.

By placing a tick (✔) in the correct box, determine which of the following statements is true:

Diogo is 18 years old. Give a reason why the regression line should not be used to estimate the number of hours Diogo watches television per week.

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.

(i)     $\overline{x}$, the mean number of hours spent on social media;

(ii)     $\overline{y}$, the mean number of IB Diploma points.

Plot the point $(\overline{x},\overline{y})$ on your scatter diagram and label this point M.

Write down the equation of the regression line $y$ on $x$ for these eight male students.

Draw the regression line, from part (e), on your scatter diagram.

Use the given equation of the regression line to estimate the number of IB Diploma points that this girl obtained.

Write down a reason why this estimate is not reliable.

Draw a scatter diagram for this data. Use a scale of 2 cm for 5000 folders on the horizontal axis and 2 cm for 10 000 Euros on the vertical axis.

Write down, for this set of data the mean number of folders produced, $\overline{x}$;

Write down, for this set of data the mean production cost, $\overline{C}$.

Label the point $\text{M}(\overline{x},\overline{C})$ on the scatter diagram.

State a reason why the regression line $C$ on $x$ is appropriate to model the relationship between these variables.

Use your graphic display calculator to find the equation of the regression line $C$ on $x$.

Draw the regression line $C$ on $x$ on the scatter diagram.

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.

Plot and label the point M$\left(\overline{m},\overline{p}\right)$ on the scatter diagram.

Draw the line of best fit, by eye, on the scatter diagram.

Using your line of best fit, estimate the physics test score for a student with a score of 20 in their mathematics test.

Write down, for this set of data the mean temperature difference from 37 °C, $\overline{x}$.

Write down, for this set of data the mean number of heartbeats per minute, $\overline{y}$.

Plot and label the point M($\overline{x}$, $\overline{y}$) on the scatter diagram.

Use your graphic display calculator to find the Pearson’s product–moment correlation coefficient, $r$.

Hence describe the correlation between temperature difference from 37 °C and heartbeat.

Draw the regression line $y$ on $x$ on the scatter diagram.

Use your graphic display calculator to write down $\overline{y}$, the mean examination score.

Use your graphic display calculator to write down r , Pearson’s product–moment correlation coefficient.

Find the exact value of m and of c for these data.

Use the regression line y on x to estimate Jerome’s examination score.

Justify whether it is valid to use the regression line y on x to estimate Jerome’s examination score.

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

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.

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.

Use your graphic display calculator to find the equation of the regression line $y$ on $x$.

Use your regression equation to estimate the cost of a flight from Hong Kong to Tokyo with Galois Airways.

Explain why it is valid to use the regression equation to estimate the airfare between Hong Kong and Tokyo.