STAT 302 Final Exam Review
These practice questions and problems should help you prepare for the final exam. Please do not feel like
you need to write out an answer for each of these questions. I recommend reading through the entire
review sheet and making sure you have an understanding of all the topics covered. I encourage you to
focus on the application questions on this review sheet. Additionally, I recommend you review the class
notes and homework.
This review sheet only covers the new material (chapters 7-8). The final exam is cumulative. I
recommend using the previous review sheets to review the old material (chapters 1-6).
Chapter 7: Inference for Numerical Data
1. What do we do when we don't know the population standard deviation, 𝜎? Why can this be a problem
for our normal confidence interval and hypothesis test procedures and what can we do to correct it?
2. What is the general formula for a confidence interval for the mean when 𝜎 is unknown?
3. What is the t-distribution? How does the shape of the t-distribution change as we increase our sample
size?
4. What are the conditions for using the t-distribution to calculate a confidence interval or conduct a
hypothesis test for the mean when 𝜎 is unknown?
5. A company is trying to determine the average time of customer service calls. In a sample of 11 random
calls, the average length of the call was 7 minutes, with a standard deviation of 4. Assume the data is
normally distributed and there are no outliers.
a. What are the df?
b. What is the associated critical value for a 90% confidence level? What is the associated critical
value for a 95% confidence level? What is the associated critical value for a 99% confidence
level?
c. Construct a 90% confidence interval for the average length of the customer service calls. Based
on this interval, would you believe that the average length of calls is 10 minutes?
d. Construct a 95% confidence interval for the average length of the customer service calls. Based
on this interval, would you believe that the average length of calls is 10 minutes?
e. Construct a 99% confidence interval for the average length of the customer service calls. Based
on this interval, would you believe that the average length of calls is 10 minutes?
f. Are the conditions met to create these confidence intervals?
6. A recent study showed that the average house price in the US is $272,000. Lauren lives in California
and believes that the average house price in her state is higher than the national average. She takes a
random sample of 32 household in California and finds that the average house price is $312,000, with a
standard deviation of 95,000. Assume the data is close to normally distributed (not strongly skewed) and
there are no extreme outliers. Conduct the appropriate hypothesis test using a 0.05 alpha level of
significance.
a.
b.
c.
d.
e.
What is the null hypothesis?
What is the alternative hypothesis?
What is α?
What is the test statistic?
What are the df?
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f.
What two values on the t-table bracket of the absolute value of our test statistic? (If the test
statistic is larger or smaller than the largest/smallest value in the row, just put the value it is larger
or smaller than.)
g. Between what two values does our p-value fall?
h. What is the appropriate decision?
i. What is the appropriate conclusion?
j. Were the conditions met to conduct the hypothesis test?
7. What are the two study designs that allow us to compare the means of 2 groups? Briefly describe both
of these.
8. If subjects are measured twice under 2 different treatment conditions or at two different times, what is
the study design?
9. When is it appropriate to use a matched pairs test?
10. For matched pairs data, what are the hypotheses?
11. For matched pairs data, what is the form of the test statistic?
12. For matched pairs data, what are the conditions necessary to do a hypothesis test or calculate a
confidence interval?
13. For matched pairs data, what is the general form of a confidence interval?
14. When is it appropriate to use an independent samples test?
15. For independent samples data, what are the hypotheses?
16. For independent samples data, what is the test statistic?
17. For independent samples data, what are the degrees of freedom?
18. For independent samples data, what are the conditions necessary to do a hypothesis test or calculate a
confidence interval?
19. For independent samples, is it appropriate to calculate a confidence interval for one of the group
means and see if the other sample mean is in that confidence interval? Why or why not?
20. For independent samples data, what is the general form of a confidence interval?
21. Label the following scenarios as a single sample, matched pairs, or independent samples. Write the
appropriate hypotheses for each hypothesis test.
i.
You collect a random sample of 24 hydrological stations in California and obtain data on the
acidity of rainwater collected at each station in 2000 and in 2010. Acidity is measured by pH
on a scale of 0-14 (the pH of distilled water is 7.0). You want to determine whether the
acidity levels between 2000 and 2010 are different (difference = 2000 acidity - 2010 acidity).
ii.
Agricultural pests can be controlled to some extend either by using pesticides to kill them or
by introducing a large number of sterilized males to diminish the species’ reproductive
potential. Ten large corn fields are treated with pesticides and ten have sterilized males
introduced. At harvest time, you compare the average corn yield for the two treatments. You
want to determine if the pesticide treatment provides a larger yield than the sterilized male
treatment (difference = sterilized male yield - pesticide yield).
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iii.
To check a new analytical method, a chemist obtains a reference specimen of a known
concentration from the National Institute of Standards and Technology. She then makes 20
measurements of the concentration of this specimen with the new analytic method. She
wants to check and see if the new method is biased by comparing the mean result with the
known concentration (c).
iv.
Another chemist is checking the same new method. He does not have access to a reference
specimen, but a familiar analytic method is available. He wants to know if the new and the
old methods agree. He takes a specimen of unknown concentration and measures the
concentration 10 times with the new method and 10 times with the old method. (difference =
new method - old method).
22. Hutchinson-Gilford progeria syndrome is a rare genetic condition that produces rapid aging in
children. As a result, cardiovascular disease is a common cause of death in the teenage years. A clinical
study examined the effect of treatment with the drug lonafarnib on a number of physiological outcomes.
Pulse wave velocity (PWV) is the standard measure of vascular stiffness, an important factor in
cardiovascular health. Researchers studied 18 children with progeria to determine how lonafarnib affected
their PWV. They measured the PWV values (in m/s) of each child at the beginning of the study
(“untreated”) and then again at the end, after taking lonafarnib for two years (“treated”). They conducted
a hypothesis test at the 0.05 significance level to determine if there was evidence that the two-year
treatment with lonafarnib lowers PWV in children with progeria. Consider the difference to be PWV
treated - PWV untreated. Assume that the children were randomly selected (case-control study) and that
the distribution of the differences is slightly right skewed with no extreme outliers. The 18 differences in
the sample have an average value of -3.917 and a standard deviation of 2.644.
a.
b.
c.
d.
e.
f.
What is the appropriate type of test?
What are the hypotheses?
What is the significance level?
What is the test statistic?
What are the degrees of freedom?
Between what two values does the test statistic fall (on the t-table)? (If the test statistic is larger or
smaller than the largest/smallest value in the row, just put the value it is larger or smaller than.)
g. What is the p-value?
h. What is the decision?
i. What is the conclusion?
j. Are the conditions met?
k. Create a 98% confidence interval for the difference between the before and after values.
23. Avandia (rosiglitazone maleate) is an oral anti diabetic drug produced by the pharmaceutical
company GlaxoSmithKline. Before a drug can be prescribed, we must know how the body absorbs and
excretes it. Patients were randomly assigned to be given a single dose of either 1 mg or 2 mg of Avandia
and the maximum plasma concentration of the drug (in ng/mL) was assessed. Is there significant evidence
at the 0.01 significance level that the maximum plasma concentration dose is dependent on dose and
higher dose results in higher concentrations (difference = 2mg - 1mg)? Assume there are no extreme
outliers in either group and that the distribution of both groups is strongly skewed right. Use the table
below which gives the treatment summary statistics.
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Summary Statistics
Treatment
n
x-bar
1 mg
32
76
2 mg
32
156
s
13
42
a.
b.
c.
d.
e.
f.
What is the appropriate type of test?
What are the hypotheses?
What is the significance level?
What is the test statistic?
What are the degrees of freedom?
Between what two values does the test statistic fall (on the t-table)? (If the test statistic is larger or
smaller than the largest/smallest value in the row, just put the value it is larger or smaller than.)
g. What is the p-value?
h. What is the decision?
i. What is the conclusion?
j. Are the conditions met?
k. Create a 90% confidence interval for the difference between the two doses.
24. What does ANOVA stand for? When do we use ANOVA?
25. Why can’t we use multiple independent samples t-tests instead of using ANOVA?
26. For an ANOVA test, what are the hypotheses?
27. For an ANOVA test, how do we get the p-value?
28. For an ANOVA, what are the conditions necessary to do a hypothesis test?
29. A dental study evaluated the effect of tooth etch time on resin bonding strength. A total of 78
undamaged, recently extracted first molars (baby teeth) were randomly assigned to be etched with
phosphoric acid gel for either 15, 30, or 60 seconds. Composite resin cylinders of identical size were
then bonded to the tooth enamel. The researchers examined the bond strength after 24 hours by
finding the failure load (in megapascal) for each bond. The summary data and the partial ANOVA
table for this experiment are below. A QQ plot showed no deviations from normality. The researchers
wanted to test at the 10% significance level whether there was an association between tooth etch time
and resin bonding strength.
Summary Statistics
Etch Time
n
x-bar
s
15 seconds
26
4.49 2.28
30 seconds
26
6.98 3.15
60 seconds
26
8.48 4.17
JMP Output
Source
Etch time
Error
Total
DF
Sum of Squares
812.745
Mean Square F-Ratio
Prob > F
0.0002
1023.953
a. What is the appropriate type of test?
b. What are the hypotheses?
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c.
d.
e.
f.
g.
h.
i.
j.
What is the significance level?
Fill in the missing spaces on the ANOVA table.
What is the test statistic?
What is the p-value?
What is the decision?
What is the conclusion?
Are the conditions met?
Based on the summary statistics, what two groups do you expect to be statistically significantly
different?
30. If we were to complete pairwise/multiple comparisons, using the Bonferroni correction, what would
we use as our modified significance level, α*?
Chapter 8: Introduction to Linear Regression
1. When do we use linear regression?
2. What is the first step in determining if there is a linear relationship between two numerical variables?
3. What does correlation, or r, measure?
4. When is it appropriate to use r?
5. What are the possible values of r?
6. What are the units of r?
7. Does r depend on the units a variable was measured in? Does r depend on which variable is defined as
the response variable?
8. The correlation between IQ score and school GPA is r = 0.634. The correlation between wine
consumption and heart disease is r = −0.645. Which of these two correlations indicates a stronger
straight-line relationship? Explain your answer.
9. The following scatterplot shows the relationship between the weight of a car and the mileage it gets.
How would you describe the association? If you were given a choice between -1.0, -0.79, -0.42, 0,
0.42, 0.79, and 1.0, which would you say is the best estimate of the correlation between these two
variables?
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10. What happens to r in the presence of outliers? For example, what would happen to r if an outlier was
added that is in line with the rest of the data? What would happen to r if an outlier was added that was out
of line with the rest of the data?
11. How do we interpret R-squared?
12. A study of class attendance and grades among first-year students at a state university showed that in
general students who attended a higher percentage of their classes earned higher grades. Class attendance
explained 25% of the variation in grade index among the students. What is the numerical value of the
correlation between the percentage of classes attended and the grade index?
13. What is 𝛽1 ? What do we use to estimate 𝛽1 ?
14. How do we interpret the value of b1?
15. What is 𝛽0 ? What do we use to estimate 𝛽0 ?
16. A researcher wanted to see if the average SAT Mathematics score of each state’s high school seniors
could be predicted by the proportion of each state’s seniors who took the exam. He found that the leastsquares regression line for predicting average SAT Math score from proportion taking is: average Math
SAT score = 580.0 (109.7 × proportion taking). Interpret the slope and the intercept of this equation. In
New York, the proportion of high school seniors who took the SAT was 0.89. Predict their average score.
17. The correlation between the average SAT Mathematics score in the states and the proportion of high
school seniors who take the SAT is r = −0.843. The correlation is negative. What does that tell us? How
well does proportion taking predict average score? (Use r2 in your answer.)
18. What is an outlier?
19. What is a high leverage point?
20. What is an influential point?
21. What are the hypotheses we test when we are doing statistical inference about linear regression?
22. For linear regression, how do we calculate the test statistic?
23. For linear regression, how do we calculate the p-value?
24. What do we use to denote the predicted response of an individual?
25. What is a residual, in regards to linear regression?
26. What is interpolation? What is extrapolation? Which one of these should we avoid?
27. A study was done to determine whether or not social exclusion causes “real pain.” Researchers
looked at a random sample of 7 individuals; brain activity in an area of the brain that responds to physical
pain to see if activity increases as distress from social exclusion increases (measured by social distress
score). The social distress scores in the experiment ranged from 0 to 10. A scatterplot shows a moderately
strong linear relationship. The table below shows the regression output. Researchers want to test whether
or not there is an association between social exclusion and brain activity in this pain center at the 0.05
level.
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a.
b.
c.
d.
e.
f.
g.
h.
i.
j.
Estimate
Standard Error
(Intercept)
-0.1261
0.02465
Distress
0.06078
0.009979
What are the hypotheses?
What is the significance level?
What is the test statistic?
What is the p-value?
What is the decision?
What is the conclusion?
What is the regression equation?
What is the predicted brain activity for a person with a social distress score of 2.0?
A person has a social distress score of 2.0 and a brain activity level of 0.15. What is their
residual?
A scientist wants to use the above regression formula to estimate the brain activity for someone
with a social distress score of 15. Is this a good idea? Why or why not?
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