Stats Worksheet

Quantitative Reasoning Exam 2 all 2022 (50 points total)
Name:____________________________
Directions: Please show all of your work where relevant. For full credit, make sure to include units in
your final answer(s), if relevant. Questions are worth one point unless otherwise noted.
Q1) For Figure 1 shown below:
(a) Describe the relationship between variables X and Y shown in the figure below. Include the
direction and strength (perfect, strong, moderate, weak, or none) of the correlation. (2 points)
(b) Other than coincidence, what are three possible explanations for the relationship between
Variable X and Y shown in the scatterplot? (3 points)
Figure 1
Figure 2
Preferred time to do various activities
(Higher scores are later in the day)
Q2) For Figure 2 shown above:
(a) Describe the scatterplot. Include the direction and strength (perfect, strong, moderate, weak, or
none) of the relationship between the specified variables.
(b) Does this scatterplot prove that anxiety level affects when people prefer to do things? Explain
(1-2 sentences). (2 points)
2
Q3) An independent research company for Consumer Reports tested whether Golden Retrievers
preferred Brand P or Brand X of dog food. They found that 67% of the 250 Golden Retrievers they tested
ate Brand P dog food when a bowl of each type of dog food was placed in front of them.
(a) What is the sample of this study?
(b) What is the sample statistic for this study?
(c) Find the estimated margin of error for the sample statistic. (Report your answer to two
significant digits.) (2 points)
(d) What is the population of this study?
(e) What is the population parameter?
(f) Write a statement describing the confidence interval to a general audience. (2 points)
(g) Can we be at least 95% confident that over 50% of all Golden Retrievers would prefer Brand P
over Brand X?
3
Q4) The axillary temperatures (taken under the armpit) of healthy newborn babies are normally
distributed, with a mean of 36.9 àand a standard deviation of 0.4 î
(a) Draw a normal curve, and label z-scores from -3 to +3 standard deviations from the mean.
Below the z-scores, label the data values of healthy newborn temperatures corresponding to the
number of standard deviations above/below the mean. (3 points)
Use the 68-95-99.7 rule to answer the following questions. (Report your answers to one decimal place.)
(b) What percentage of newborns have temperatures that are less than 37.7 ÿ
(c) What percentage of newborns have temperatures that are between 36.9 and 37.3 ÿ
(d) What temperature is higher than 16% of newborn temperatures?
Use the z-table to:
(e) Find the percentage of newborns whose temperatures are lower than 36.0 î
(f) Find the percentage of newborns whose temperatures are higher than 37.5 î
(g) Find the temperature that is higher than the temperatures of 95% of newborns (Q1).
(h) You are a nurse at a hospital. A newborn is admitted for observation. You find that her axillary
(under armpit) temperature is 35.7 î How likely is it that this newbornàtemperature comes
from the distribution for healthy newborns? That is, what is the percentage of healthy newborns
whose temperatures are less than (or equal to) 35.7 ÿ
(i) Is this a ôatistically significant event(in which case you should notify the doctor)?
4
Q5) A newly-developed drug designed to lower diastolic blood pressure (pressure when the heart is
relaxed) was independently evaluated by the FDA. In a double-blind experimental study, 500 people
with high diastolic blood pressure were randomly assigned to either the new drug (experimental) group
or placebo pill (control) group.
After 6 months of taking the new drug or placebo pill, all study participants were given a physical
examination. The mean diastolic blood pressure of the 250 participants in the control group was 90 mm
Hg.
(a) What is the null hypothesis for this study? (2 points)
(b) What is the alternative hypothesis for this study? (2 points)
The mean diastolic blood pressure among the 250 people in the experimental group was 85. The chance
of getting this blood pressure if there were no difference between groups (or from the blood pressure
distribution of the control group, shown below) is 2%.
Distribution of temperatures in the control group:
Mean:
90 mm Hg
2%
-3
-2
-1
0
1
2
3
(c) What is the appropriate conclusion to draw from these results? (2 points)
(d) Do you think the drug company who developed this drug would be pleased with the results of
this study? Explain (1-2 sentences).
(e) If the chance of getting this blood pressure (if there were no difference between groups) were
instead 15%, what would the appropriate conclusion be?
5
Q6) The percentages of young people (18-29) who voted in six U.S. presidential elections from 2000 ²020 are (in no particular order):
¶6.3%, 59%, 63.8%, 63.6%, 61.8%, 61.4%
For all relevant questions, report your answer to one decimal place.
(a) Find the 5-number summary for this data. (5 points)
(b) Draw a boxplot for this data. (2 points)
(c) Based on the shape of the boxplot, what is your best estimate for the shape of the distribution
of young voter turnout for all presidential elections?
(d) Which measure of central tendency (mean, median, or mode) is most appropriate to use to
describe this data? Explain why. (2 points)
(e) Use the Range rule of Thumb to estimate the standard deviation. (2 points)
(f) The actual standard deviation is 2.50%. What is the relative error of the estimated standard
deviation using the Range Rule of Thumb?
(g) If the percentage of young voters in 2024 is 72%, would the standard deviation of the
percentages of young voters from 2000 2024 be less than, greater than, or about the same as
the standard deviation of young voters from 2000 2020 (2.50%)? Explain (1-2 sentences). (You
don have to do any calculations to answer.)

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