Disclaimer: These questions are designed to test both your ability to solve hypothesis
testing problems (the first half) and your conceptual understanding of some of the concepts
that underlie hypothesis testing (the second half). However, this should not be viewed as a
comprehensive study guide, and there is no guarantee that anything included within will be
relevant for the final exam.
Computational questions
1.
You are a TA for an undergraduate statistics course who leads two discussion sections
each week. After the class midterm, you are curious as to whether your students differed
from the rest of the class. The population of students who were
not
in your sections got
an average of 57 points with a standard deviation of 8 points. Students in your sections,
which have a total of 60 people in them, got an average of 55 points. Conduct the
appropriate hypothesis test, at
"
=.05, to determine whether students in your sections
performed differently than the class average. Provide the information indicated below:
(a)
Research problem
(b)
Statistical hypotheses
(c)
Decision rule
(d)
Calculations
(e)
Decision
(f)
Interpretation
2.
Construct a 95% confidence interval for the population mean of the midterm scores of
students in your sections, and provide an interpretation.
3.
Since you are secretly convinced that you are the best TA in the class, you are determined
to find statistical evidence that shows that students in your sections do better than those in
other sections. You decide, quite reasonably, that the only students who might be
benefiting from your incredible teaching skills are those who actually attend section.
After secretly taking attendance by checking to see who picked up their homeworks from
the pile, you determine that 15 students regularly show up to your sections. These
students got an average of 62 points on the midterm, with a standard deviation of 6
points. Conduct the appropriate ttest, at
"
=.05, to determine whether students who
regularly attended your sections performed better than the class average. Provide the
information indicated below:
(a)
Research problem
(b)
Statistical hypotheses
(c)
Decision rule
(d)
Calculations
(e)
Decision
(f)
Interpretation
4.
Every year, Peter and Peggy Piper pick a peck of pickled peppers. And, every year, they
argue about who is better at picking pickled peppers. After decades of squabbling, the
Pipers come to you, a noted statistician, and ask for your help in resolving their dispute.
Here are the number of pecks of pickled peppers they picked each of the last seven years:
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Peggy Piper
Peter Piper
17
10
25
14
22
7
19
12
15
18
22
6
23
3
(Assume that the underlying populations are normally distributed, with equal variances.)
Conduct the appropriate hypothesis test, at
"
=.05, to determine whether Peggy and Peter
Piper pick different numbers of pecks of pickled peppers. Provide the information
indicated below:
(a)
Research problem
(b)
Statistical hypotheses
(c)
Decision rule
(d)
Calculations
(e)
Decision
(f)
Interpretation
5.
Construct a 99% confidence interval for the population mean of the difference in the
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 Fall '08
 Ard
 Normal Distribution, Statistical hypothesis testing, Peter Piper, Peggy Piper

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