Download STA 200 Exam II Spring 2004

STA 200
Exam II
Spring 2004
Instructions
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Please put your name and section number (e.g. 200004) on the bubble sheet provided
and on the front page of this exam packet.
For each problem on this exam, please choose the best answer and clearly mark it on
bubble sheet.
No questions please, except those designed to inquire about possible errata.
Problems 1-32 are worth 3 points each. Problem 33 is worth 4 points.
Turn in this exam when you turn in the bubble sheet.
In the table below we have donations (in dollars) for a subset of fraternities and sororities at U.K., as
reported in the fall of 2003. The next three questions concern these data.
Donations
Fraternity or Sorority
(in dollars)
Alpha
Gamma
Rho
500
Sigma
Phi
Epsilon
500
Alpha
Delta
Phi
870
Lambda
Chi
Alpha
1800
Sigma
Chi
1000
Phi
Sigma Kappa
300
Sigma
Pi
400
Sigma
Kappa
2010
Delta
Zeta
10000
Sigma
Alpha Epsilon
0
Pi
Kappa
Alpha
100
Phi
Gamma Delta
0
Alpha
Tau
Omega
600
Pi
Beta
Phi
1500
1. The median donation (in dollars) is
a. 500
b. 550
c. 1205
d. 600
2. The lower (first) quartile of the donations is
a. 300
b. 500
c. 1500
d. 1800
3. The upper (third) quartile of the donations is
a. 300
b. 500
c. 1500
d. 1800
4. A dishonest butcher has a scale on which he weighs the meat his customers buy. In order to
increase his profits, he has altered the scale so that it always reads almost exactly 10 percent more
than the actual weight. The measurements from this scale are
a. biased and unreliable
b. biased and reliable
c. unbiased and unreliable
d. unbiased and reliable
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5. A large group of college students work as clerks at a local boutique. Their median hourly salary is
$12.00 and the average hourly salary there is $8.50. Management decides to give everyone a flat
0.75 cent per hour raise. What is the new median salary?
a. the new median is $12.75
b. can't tell unless you know everyone else's salaries
c. the median is still $12.00 since it is not affected by changes such as raises
d. much closer to the mean than it was before
6. A large group of college students work as clerks at a local boutique. Their median hourly salary is
$12.00 and the average hourly salary there is $8.50. Management decides to give everyone a flat
0.75 cent per hour raise. What is the new standard deviation? Remember, the standard deviation
just measures how spread out the data are.
a. the same as it was before the raise
b. can't tell unless you know everyone else's salaries
c. it is 0.75 cents larger
d. it is (12+17.50)/2 = $14.75 larger
7. A large group of college students work as clerks at a local boutique. Their median hourly salary is
$12.00 and the average hourly salary there is $8.50. What do you know about the salary structure
at this boutique?
a. only about 25% of the clerks make above the median salary
b. at least one or two people at the store must make very high hourly wages
c. that the distribution of salaries at the boutique is most likely skewed, with the tail to the left
d. that a five number summary would not be a good way to summarize these data
8. If the mean of a list of numbers is 16.7 and the standard deviation is 0, then
a. there must have been an arithmetic mistake.
b. all of the numbers on the list are equal to 16.7.
c. all of the numbers on the list are the same, but their common value can be anything.
d. 68% of the numbers on the list are between -16.7 and +16.7
e. 68% of the numbers on the list are between 0 and 33.4.
9. If you calculate the standard deviation of a set of numbers and get a negative number you can
conclude that
a. the mean must be 0.
b. you made an arithmetic mistake.
c. all of the numbers are the same.
10. The scores on the final exam in a statistics course are close to being normally distributed. The
mean score is 60 points, and two-fifths of the class score between 45 and 75. What can you say
about the standard deviation of the scores?
a. it’s larger than 15 points
b. it’s smaller than 15 points
c. nothing definitive from the information given
d. it is ½ point: (75-45)/60 = ½ point
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Here is a boxplot of the number of new members joining U.K’s fraternities and sororities for Fall 2004.
The next three problems refer to this plot.
Fraternities and Sororties at U.K. Fall 2003
Number of New Members
120
100
80
60
40
20
0
11. This plot show that
a. about 50% of all the fraternities and sororities enrolled fewer than roughly 45 members
b. about 50% of all the fraternities and sororities enrolled between 20 and 40 members
c. about 75% of all the fraternities and sororities enrolled more than roughly 45 members
d. about 75% of all the fraternities and sororities enrolled fewer than roughly 45 members
12. We see from the plot that the median number of new members is about
a. 18
b. 8
c. 100
d. 44
13. The box in the boxplot marks
a. the full range covered by the data
b. the range covered by the middle half of the data
c. the range covered by the middle three-quarters of the data
d. the span one standard deviation on each side of the mean
e. the span two standard deviations on each side of the mean
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Below are the ACT sub scores for Pre/Elementary Algebra as reported by the 2000 ACT National Score
Report on their website. The next three questions concern these data. Make sure you know what is in the
Table. There are 1,065,138 ACT sub scores there: 27,191 were 18’s, 26,448 were 5’s, etc.
ACT
Sub
Score
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
Number of
Students
Receiving Listed
Sub Score
27191
48841
38946
50760
89749
103571
90955
91181
130291
113841
104998
81081
52945
26448
8493
4656
1033
158
14. What is the median of these ACT scores?
a. 9.5
b. 130291
c. 3.5
d. 11.0
15. What is the lower quartile of these ACT scores?
a. 8.0
b. 26448
c. 637
d. 5.0
16. About what percentage of all of these students had ACT sub
scores bigger than 11?
a. About 16%
b. about 20.0%
c. about 42.0%
d. about 1.6%
17. The standard deviation is fine as a way of measuring spread when
a. the distribution is statistical
b. it is also used to measure center
c. the distribution is symmetric
d. the distribution is skewed
18. Suppose that adult women in China have heights which are normally distributed with mean 157
centimeters and standard deviation 8 centimeters. Adult women in Japan have heights which are
normally distributed with mean 158 centimeters and standard deviation 6 centimeters. Which
country has the higher percentage of women taller than 167 centimeters? Use Table B if
necessary.
a. China
b. Japan
c. The percentages are the same.
d. It is not possible to tell from the information given.
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19. IQs among undergraduates at Mountain Tech are approximately normally distributed. The mean
undergraduate IQ is 110. About 99.7% of undergraduates have IQs between 95 and 125. Using the
68-95-99.7 it is clear that the standard deviation of these IQs is about
a. 5
b. 10
c. 15
d. 20
e. 25
20. The heights of American men aged 18 to 24 are normally distributed with mean 68 inches and
standard deviation 2 inches. So 10% of all young men in this age category are taller than what?
Use Table B if you need to.
a. 68 inches
b. 70½ inches
c. 73 inches
d. 75½ inches
21. The heights of American men aged 18 to 24 are normally distributed with mean 68 inches and
standard deviation 2 inches. Using the 68-95-99.7 Rule, we can say that about 95% of all young
men have heights between
a. 65.5 inches and 70.5 inches
b. 64 inches and 72 inches
c. 60.5 inches and 75.5 inches
d. 58 inches and 78 inches
22. The EPA says that the level of statistical contamination in students' minds follows a normal
distribution with a mean of 10 ppbc (parts per brain cell) and a standard deviation of 1.24 ppbc.
Suppose a student is chosen at random and tested for statistical contamination. What is the
probability that this student will have contamination levels between 8 and 11.5 ppbc? Use Table
B.
a.
b.
c.
d.
about 83 chances in 100
between 8 and 11.5 chances in 100
about 17 chances in 100
about 34 chances in 100
23. You are a high school social studies teacher teaching both a 1st hour regular class (100 students)
and a 2nd hour honors class (50 students). The honor class mean is 281, and the honor class
standard deviation is 18.54. The regular class mean is 201 and the regular class standard
deviation is 65.17. Both sets of class scores are assumed to follow a normal distribution. Tom is a
member of the regular class and has a score of 285. Tom wants to transfer to the honors class.
About what proportion of students in the honors class have scores higher than Tom?
a. about 0.22; so somewhere around 2.2%
b. about 0.22; so somewhere around 22%
c. about 0.42; so somewhere around 42%
d. about 0.42; so somewhere around 4.2%
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Scores on the Wechsler Adult Intelligence Scale for the all seniors in the 70 to 74 age group are
approximately normally distributed with mean 90 and standard deviation 25. Use the 68-95-99.7 Rule to
answer the next three questions.
24. Mrs. Jones, who is 72, scores 140 on the test. What is Mrs. Jones' standard score?
a. -2.00
b. 1.4
c. 2.00
d. none of the above
25. About what percentage of all individuals in this age group score higher on the test than Mrs.
Jones?
a. 5.0%
b. 2.5%
c. 95%
d. can’t tell from information given
26. Mrs. Jones' neighbor, Miss Johnson, who is 73, was told that only 16% of the seniors in her age
group scored higher on the test than she did. What was her score?
a. 115.0
b. 140.0
c. 90
d. none of the above
27. January 2004 sales at Keeneland in Lexington, Kentucky recorded an average sale price of
$39,225 and a median sale price of $13,000. What can you say about the distribution of January’s
sale prices?
a. it is surely symmetric
b. it is surely skewed, with the tail to the left
c. it is surely skewed, with the tail to the right
d. it is surely bell-shaped
28. Have a look at the following distribution. What would be the preferred summary of these data?
a. five-number summary
b. mean and standard
deviation
c. standard score and
variance.
d. can't tell from the
information given
e.
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29. The
weights
of
dormitory
cockroaches follow a normal
distribution with mean 80 grams
and standard deviation 2 grams.
The figure to the right is the
normal curve for this distribution
of weights, divided into sections
each of width one standard
deviation. Point A below this
normal curve corresponds to:
a. 68 grams
b. 72 grams
c. 74 grams
d. 76 grams
30. Refer to the cockroach curve just
above. About what percentage of all cockroaches have weights that are between points C and F on
the curve?
a. 81.5%
b. 68%
c. 99.7%
d. 95%
31. The length of pregnancy isn't always the same. In pigs, the length of pregnancies varies according
to a normal distribution with mean 114 days and standard deviation 5 days. The median length of
a pig pregnancy is:
a. 119 days.
b. 114 days.
c. 109 days.
d. between 109 and 119 days, but can't be more specific.
e. greater than 114 days, but can't be more specific.
32. The length of pregnancy isn't always the same. In pigs, the length of pregnancies varies according
to a normal distribution with mean 114 days and standard deviation 5 days. About what
proportion of all pig pregnancies last more than 122.5 days? Use Table B if you need to.
a. about 4.5%
b. about 95.5%
c. about 9.5%
d. about 90.5%
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33. (4 points) Transition Problem: An SRS of 156 U.K. students is taken and each one is asked “Do
you agree with President Bush's policy toward North Korea?” Suppose 53% in your sample said
“yes.” Suppose, also, that you are reminded that the sampling distribution of the sample proportion
is a normal distribution with mean given by p, the true proportion of ALL U.K. students who
would have said “yes”, and that the standard deviation is
p(1 − p)
.
156
If we assume that p is really 0.5 (that is, 50%), then how likely are you to see a statistic that
is 53% or larger?
a. About 75 times in 100
b. About 53 times in 100
c. About 22 times in 100
d. About 1 time in 100
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