Probability and Statistics
Review Questions for Final Exam
Because the final covers so much material the problems will often be easier than on past exams,
for instance with more questions on concepts than in the past. However, the flip side is that there
will be little room for partial credit. Expect questions of a similar level to those on this review,
with only a few questions of the level of problem #5.
Included here are questions on new material only. For old material please review previous exams,
review questions and quizzes. The exam is comprehensive, with roughly 25% on material from each
of Exam 1, Exam 2, Exam 3 and new material. To inflate my undersized ego I have decided to assert
my authority and oppose popular opinion by making the exam open book and closed notes (and you
cannot put tabs marking pages in the book; use the Table of Contents to find things). However, you
can also bring a 3Ć5notecard with notes on both sides if you feel the need. A calculator may be
used, but cannot be used to avoid work (e.g. you must still use Z-scores).
(1): Suppose a random sample of size n= 9 is drawn from a normal distribution with Āµ= 20.0.
For what value of kis
PĀµĀÆ
ĀÆ
ĀÆ
ĀÆ
Yā20.0
S/ā9ĀÆ
ĀÆ
ĀÆ
ĀÆā„kĀ¶= 1%
and for what value of kis
PĀµĀÆ
ĀÆ
ĀÆ
ĀÆ
Yā20.0
Ļ/ā9ĀÆ
ĀÆ
ĀÆ
ĀÆā„kĀ¶= 1%
(2): Suppose a sample of size n= 7 from a normally distributed variable Yhas sample average
ĀÆy= 17.
a. Give the 95% confidence interval for the mean value ĀµYif the sample standard deviation is
S= 2.75.
b. Give the 95% confidence interval for the mean value ĀµYif the actual standard deviation is
known to be Ļ= 2.75.
c. Use the sample data to test the hypothesis
H0:Āµ= 15
H1:Āµ > 15
at the Ī±= 0.05 level, if the sample standard deviation is S= 2.75.
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