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Practice Exam 1 Solutions
Final Examination
Directions
The exam will end 3 hours minutes after it begins. The exam is divided into two parts.
The first part is multiple choice. Please answer the multiple choice questions on the exam
by circling the
best
answer (some rounding occurs in several places). The second part of
the exam consists of several problems. Please answer these problems in the space
provided on the exam (you may use the backs of the sheets if necessary). You will get
partial credit for these problems
provided
that your answers are organized and legible so
that your train of thought can be easily followed. All answers must also be transferred to
the answer sheet to be fully counted.
Good Luck
DON'T EVEN THINK ABOUT PANICING
By
Printing
my name below I acknowledge that Harvard has an honor code and that I
will adhere to it. Failure to abide by the honor code could result in failing this course and
having to wash Professor Parzen’s car with my toothbrush.
NAME
: ______________________________________________ (50 if not printed)
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1)
A hypothesis test is used to prevent a machine from underfilling or overfilling
quart bottles of beer. On the basis of a sample, the null hypothesis is rejected and
the machine is shut down for inspection. A thorough examination reveals there is
nothing wrong with the filling machine. From a statistical point of view:
a. A correct decision was made.
b. A Type I and Type II error were made.
c.
A Type I error was made.
d. A Type II error was made.
2)
The median waiting time for patients to see a doctor at a local emergency room is
much smaller than the mean waiting time. Which of the following is most
consistent with this information (circle one):
a. A histogram of the waiting times would be symmetric.
b. A histogram of the waiting times would be leftskewed.
c.
A histogram of the waiting times would be rightskewed.
3)
A student is studying very hard in a fluid dynamics course, but he knows he will
either pass or not pass. Suppose this student, Jack Daniels, has a probability of
0.90 for studying the night before the exam. Also, he has a probability of 0.75 for
passing the exam. If the probability of passing the exam, given that he studied the
night before, is 0.82, what may you conclude?
a. The probability of Jack not passing the exam is 0.10.
b. P(Jack studies OR Jack passes) is greater than 0.75.
c. P(Jack does not pass AND Jack studies) is greater than 0.5.
d. P(Jack passes AND Jack studies) is greater than 0.75.
e. None of the above
4)
Suppose a computer processor yielded the following random sample of binary
digits:
0101001101010100010000010101010001011010
01010010010101010100110001011010
Is the computer processor yielding an even distribution of ones and zeros? If the
above sample contains 72 digits, of which thirty are “ones”, what is the value of
the test statistic to answer this question?
a.
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This note was uploaded on 03/27/2012 for the course STATS 104 taught by Professor Michaelparzen during the Fall '11 term at Harvard.
 Fall '11
 MichaelParzen

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