ch 20 practice test
1a. [2 marks]
A survey investigated the relationship between the number of cleaners, , and the amount of time, , it
takes them to clean a school.
Use your graphic display calculator to write down the equation of the regression line on .
1b. [2 marks]
Write down the value of the Pearson’s product–moment correlation coefficient, .
1c. [2 marks]
Use your regression equation to find the amount of time 4 cleaners take to clean the school. Is this
interpolation or extrapolation?
2a. [1 mark]
As part of his IB Biology field work, Barry was asked to measure the circumference of trees, in
centimetres, that were growing at different distances, in metres, from a river bank. His results are
summarized in the following table.
State whether distance from the river bank is a continuous or discrete variable.
2b. [4 marks]
On graph paper, draw a scatter diagram to show Barry’s results. Use a scale of 1 cm to represent 5 m
on the x-axis and 1 cm to represent 10 cm on the y-axis.
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2c. [2 marks]
Write down
(i) the mean distance, , of the trees from the river bank;
(ii) the mean circumference, , of the trees.
2d. [2 marks]
Plot and label the point
on your graph.
2e. [4 marks]
Write down
(i) the Pearson’s product–moment correlation coefficient, , for Barry’s results;
(ii) the equation of the regression line on , for Barry’s results.
2f. [2 marks]
Draw the regression line on
on your graph.
2g. [2 marks]
Use the equation of the regression line on
to estimate the circumference of a tree that is 40 m
from the river bank. Is this interpolation or extrapolation?
2g(part 2). [2 marks] Give an example of using the regression equation that involves extrapolation. Why is
this not desirable?
2h. [2 marks]
How many trees had a distance that was more than 1 standard deviation above the mean?
3a. [2 marks]
The scores obtained by five candidates in Mathematics and Physics examinations are given below.
Write down the correlation coefficient, , for the examination scores.
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3b. [2 marks]
Write down the equation of the regression line,
on
, for the examination scores of the five candidates.
3c. [2 marks]
A sixth candidate scored 72 in the Mathematics examination. Use the regression line,
on , to estimate his score
on the Physics examination. Is this interpolation or extrapolation?
4a. [4 marks]
The heat output in thermal units from burning
of wood changes according to the wood’s percentage
moisture content. The moisture content and heat output of
blocks of the same type of wood each weighing
were measured. These are shown in the table.
Draw a scatter diagram to show the above data. Use a scale of
to represent
to represent
on the x-axis and a scale of
thermal units on the y-axis.
4b. [2 marks]
Write down(i) the mean percentage moisture content,
;(ii) the mean heat output,
.
4c. [2 marks]
Plot the point
on your scatter diagram and label this point M .
4d. [2 marks]
Write down the product-moment correlation coefficient,
.
4e. [2 marks]
The equation of the regression line
on
is
. Draw the regression line
on
on your
on
is
. Estimate the heat output in thermal units
scatter diagram.
4f. [2 marks]
The equation of the regression line
of a
block of wood that has
moisture content.
4g. [2 marks] The equation of the regression line
is appropriate to use the regression line
on
on
is
. State, with a reason, whether it
to estimate the heat output in part (f).
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