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STA258 Week 10 Practice Questions
Solution
1. 20 toddlers were observed over several months at a nursery school. “Time” is the average number of
minutes a child spent at the table when lunch was served. “Calories” is the average number of calories
the child consumed during lunch, which was calculated from careful observation of what the child ate
each day.
a. Refer to the scatterplot of calories consumed during lunch time and time (in min) spent at the lunch
table. Describe the overall pattern of this plot. That is, describe the direction, form, and strength of the
relationship between the two variables.
There appears to be a moderate to strong negative
linear association between the number of calories consumed
by children during lunch and the average time (in minutes)
that they spent at the lunch table.
Longer time spent at the lunch table are associated with
less number of calories consumed at the lunch table.
As time (in min) spent at the lunch table increases, the
number of calories consumed tends to decrease.
b. Suppose a researcher wants to investigate the relationship between the calories consumed during lunch
time and time (in min) spent at the lunch table. Identify the response variable and the explanatory
variable in the context of this study.
Response variable: Calories consumed during lunch time
Explanatory variable: Time spent at the lunch table
c. The estimated correlation coefficient, = -0.65. Interpret this number in the context of this problem.
If a child’s time spent at the lunch table is one standard deviation above the mean, their number of
calories spent during lunch time is 0.65 standard deviation below the mean of number of calories
consumed during lunch time.
3. A study finds that high school students who have a computer at home get higher grades on average than
students who do not. Does this mean that parents who can afford it should buy a computer to enhance
their children's chances of academic success? Briefly explain/justify your answer.
Not necessarily. While it is possible that some students are doing better academically and therefore
getting int university because of their computers, it is also possible that their parents have enough
money to buy them a computer, and also enough money to pay for their education. It may be that
academically able student who is more likely to go to university will want a computer more, and
therefore be more likely to get one somehow. Therefore, the study does not provide good evidence that
a computer at home will enhance chances of academic success.
4. The United Nations Development Programme (UNDP) uses the Human Development Index (HDI) in an
attempt to summarize in one number, the progress in health, education, and economics of a country. The
gross domestic product per capita (GDPPC) is used to summarize the overall economic strength of a
country. Below is a scatterplot of GDP per capita against HDI for 169 countries throughout the world.
a. Is it appropriate to summarize the strength of association with a correlation? Answer Yes or No.
Briefly Explain/Justify your answer.
It is not appropriate to summarize
the strength of the association
between GDP per capita and HDI value
with a correlation, since the association
is not linear (e.g., exponential).
b. GDPPC is measured in dollars. Incomes and other economic measures tend to be highly right
skewed. Taking logs often makes the distribution more unimodal and symmetric. Suppose that we
use the log re-expression to make a scatterplot of log(GDPPC) against HDI. Comment on the effects
of re-expression.
The plot is much straighter than the original.