MATH302 Statistics�Final Examination

Name: MATH302 Statistics�Final Examination
Brand: American Public University
Price: 2 USD
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Author: Isabella White

Final exam for statistics.

Isabella White

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Statistics—MATH302
Final Examination
INSTRUCTIONS:
This is an open-book and open note examination. You may use your textbook, notes, your
computer and a calculator during the examination. However, you are not to consult—in any
manner--with anyone while you complete this examination. Absolutely no collaboration is
permitted on this examination.
This examination consists of this cover sheet and 7 consecutively numbered pages. There are
25 questions. Each question on this exam has the same weight—four points—and this
examination will count as 20% of your final grade for the course.
AFTER you have answered all of the questions posed in this examination, you are to upload
your answers into the Final Exam Shell in the Exams section of our online course. DO NOT
access the Final Exam Shell until AFTER you have formulated your answers to all of the
questions on this examination. Remember, you will be able to access the Final Exam Shell
only once.
You must enter your answers into the Final Exam Shell in the Exams section of our course
by 11:59PM Eastern Time on the due date noted in the course calendar and in the
Announcements section of our online classroom. No late submissions will be accepted.

1
1. A lawyer researched the average number of years served by 45 different justices on the
Supreme Court. The average number of years served was 13.8 years with a standard
deviation of 7.3 years. What is the 95% confidence interval estimate for the average number
of years served by all Supreme Court justices? Place your limits, rounded to 1 decimal
place, in the blanks. When entering your answer into the Final Exam Shell do not use any
labels or symbols. Simply provide the numerical values. For example, 12.3 would be a
legitimate entry.
Lower limit (first blank) = _____11.7___, Upper limit (second blank) = ___15.9____.
2. Some defendants in criminal proceedings plead guilty and are sentenced without a trial,
whereas others who plead innocent are subsequently found guilty and then are sentenced. In
recent years, legal scholars have speculated as to whether sentences of those who plead guilty
differ in severity from sentences for those who plead innocent and are subsequently judged
guilty. Consider the data given below on defendants accused of robbery, all of whom, by the
way, had previous prison records. At the .01 level of significance, do these data suggest that
the proportion of all defendants in these circumstances who plead guilty and are sent to
prison differs from the proportion who are sent to prison after pleading innocent and being
found guilty?
Plea
Guilty Not Guilty
Number judged guilty n1 = 191 n2 = 64
Number sentenced to prison x1 = 101 x2 = 56
Sample proportion 1
ˆ = .529p 2
ˆ = .875p
A. No, because the test value -1.96 is inside the interval (-2.58, 2.58)
B. No, because the test value -4.94 is outside the interval (-1.96, 1.96)
C. Yes, because the test value -4.94 is outside the interval (-2.58, 2.58)
D. Yes, because the test value 2.58 is inside the interval (-4.94, 4.94)
Solution: C. Yes, because the test value -4.94 is outside the interval (-2.58, 2.58)
3. Serum ferritin is used in diagnosing iron deficiency. In a study conducted recently
researchers discovered that in a sample of 28 elderly men the sample standard deviation of
serum ferritin was 52.6 mg/L. For 26 younger men the sample standard deviation was 84.2
mg/L. At the .01 level of significance, do these data support the conclusion that the ferritin
distribution in elderly men has a smaller variance than in younger men?
A. No, because the test value 1.60 is less than the critical value of 2.54
B. Yes, because the test value 2.56 is greater than the critical value of 2.54
C. Yes, because the test value 0.390 is less than the critical value 2.54
D. Yes, because the test value 2.56 is greater than the critical value 0.394

2
Solution: B. Yes, because the test value 2.56 is greater than the critical value of 2.54
4. The data presented in the table below resulted from an experiment in which seeds of 5
different types were planted and the number of seeds that germinated within 5 weeks after
planting was recorded for each seed type. At the .01 level of significance, is the proportion
of seeds that germinate dependent on the seed type?
Seed Type
Observed Frequencies
Germinated Failed to Germinate
1 31 7
2 57 33
3 87 60
4 52 44
5 10 19
A. Yes, because the test value 16.86 is greater than the critical value of 13.28
B. Yes, because the test value 16.86 is less than the critical value of 14.86
C. No, because the test value 16.86 is greater than the critical value of 13.28
D. No, because the test value 13.28 is less than the critical value of 16.86
Solution: A. Yes, because the test value 16.86 is greater than the critical value of 13.28
5. A manufacturer of flashlight batteries took a sample of 13 batteries from a day’s production
and used them continuously until they failed to work. The life lengths of the batteries, in
hours, until they failed were: 342, 426, 317, 545, 264, 451, 1049, 631, 512, 266, 492, 562,
and 298. These data are also available in the worksheet Batteries in the Excel workbook
MATH302_Final.xls.
At the .05 level of significance, is there evidence to suggest that the mean life length of the
batteries produced by this manufacturer is more than 400 hours?
A. No, because the p-value for this test is equal to .1164
B. Yes, because the test value 1.257 is less than the critical value 1.782
C. No, because the test value 1.257 is greater than the critical value 1.115
D. Yes, because the test value 1.257 is less than the critical value 2.179
Solution: A. No, because the p-value for this test is equal to .1164
6. A survey of 85 families showed that 36 owned at least one DVD player. Find the 99%
confidence interval estimate of the true proportion of families who own at least on DVD
player. Place your limits, rounded to 3 decimal places, in the blanks. When entering your
answer into the Final Exam Shell do not use any labels or symbols other than the decimal
point. Simply provide the numerical values. For example, 0.123 would be a legitimate entry.
Lower limit (first blank) = __0.285________, Upper limit (second blank) = ____0.562_____.

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American Public University

Subject

Statistics

MATH302 Statistics�Final Examination

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