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About the test. 35 questions, all multiple choiceFairly even split among Units 1, 2, 3, and 4 (CH 14
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1. Stats: Modeling the World Fall Semester Review
2. About the test 35 questions, all multiple choice
Fairly even split among Units 1, 2, 3,
and 4 (CH 14 & 15).
3. #1 IQs among undergraduates at Mountain Tech are approximately normally distributed. The mean undergraduate IQ is 110. About 95% of undergraduates have IQs between 100 and 120. The standard deviation of these IQs is about
A) 25. B) 5. C) 20. D) 15. E) 10.
4. #2 The least-squares regression line is fit to a set of data.
If one of the data points has a positive residual, then
A) you have over predicted the response variable.
B) you have under predicted the response variable.
C) you have under predicted the explanatory variable.
D) you have over predicted the explanatory variable.
E) you have only predicted positive values.
5. #3 Suppose we fit the least-squares regression
line to a set of data. If a plot of the residuals shows
a curved pattern,
A) a straight line is not a good summary for the data.
B) the correlation must be 0.
C) outliers must be present.
D) r 2 = 0.
E) the correlation must be positive
6. #4 A quality control inspector on an assembly line making microwave ovens randomly chooses one of the first ten ovens manufactured each day. This oven and every tenth oven thereafter gets inspected. This is called
A) a completely randomized design.
B) stratified random sampling.
C) convenience sampling.
D) systematic random sampling.
E) simple random sampling.
7. #5 Light bulbs produced at the Lenin Electrical Works factory in
Volgagrad are defective with probability .12. To simulate the
event that a single light bulb produced at the Lenin Electrical
Works is defective, the CIA could use two digits from a
random generator with the convention
A) 00, 01, 02, ..., 85, 86, 87 > nondefective
88, 89, 90, ..., 97, 98, 99 > defective
B) 00, 01, 02, ..., 09, 10, 11 > defective
12, 13, 14, ..., 97, 98, 99 > nondefective
C) 01, 02, 03, ..., 10, 11, 12 > defective
13, 14, 15, ..., 98, 99, 00 > nondefective
D) any of the above.
E) none of the above.
8. #6 You want to take an SRS of 50 of the 816 students who
live in a dormitory on campus. You label the students 001
to 816 in alphabetical order. In the table of random
digits you read the entries
95592 94007 69769 33547 72450 16632 81194
The first three students in your sample have labels
A) 400, 769, 769. D) 559, 294, 007.
B) 929, 400, 769. E) 955, 929, 400.
C) 400, 769, 335.
9. #7 If the test scores of a class of 30 students
have a mean of 75.6 and the test scores of
another class of 24 students have a mean of
68.4, then the mean of the combined group is
a. 72
b. 72.4
c. 72.8
d. 74.2
e. None of these
10. #8 A random survey was conducted to determine
the cost of residential gas heat. Analysis of
the survey results indicated that the mean
monthly cost of gas was $125, with a standard
deviation of $10. If the distribution is
approximately normal, what percent of homes
will have a monthly bill of more than $115?
a. 34% b. 50% c. 68%
d. 84% e. 97.5%
11. #9 The average life expectancy of males in a
particular town is 75 years, with a standard
deviation of 5 years. Assuming that the
distribution is approximately normal, the
approximate 15th percentile in the age
distribution is:
a. 60 b. 65 c. 70
d. 75 e. 80
12. #10
13. #11 Given a set of ordered pairs (x, y) so that Sx=1.6, Sy=0.75, and r=0.55, what is the slope of the LSRL?
a) 1.82
b) 1.17
c) 2.18
d) 0.26
e) 0.78
14. #12 There is an approximate linear relationship between the height of
females and their age (from 5 to 18 years) described by:
height = 50.3 + 6.01(age) where height is measured in cm and age in
years. Which of the following is not correct?
a. The estimated slope is 6.01 which implies that children increase
by about 6 cm for each year they grow older.
b. The estimated height of a child who is 10 years old is about 110 cm.
c. The estimated intercept is 50.3 cm which implies that children
reach this height when they are 50.3/6.01=8.4 years old.
d. The average height of children when they are 5 years old is
about 50% of the average height when they are 18 years old.
e. My niece is about 8 years old and is about 115 cm tall. She is taller
than average.
15. #13 A random sample of 35 world-ranked chess players provides hours of study with a mean of 6.2 and standard deviation of 1.3 to winnings with a mean of $208,000 and standard deviation of $42,000. The correlation coefficient is 0.15. Find the equation of the LSRL.
a. Winnings = 4850(Hours) + 178,000
b. Winnings = 6300(Hours) + 169,000
c. Winnings = 31,200(Hours) + 14,550
d. Winnings = 32,300(Hours) + 7750
e. Winnings = 42,000(Hours) - 52,400
16. #14 In a particular rural region, 65% of the residents are
smokers, and research indicates that 15% of the smokers
have some form of lung cancer. The probability that a
resident is a smoker and has lung cancer is
0.0975
0.2308
0.15
0.65
0.0525
17. #15 Suppose that, in a certain part of the world, in any 50
year period, the probability of a major plague is 0.39,
the probability of a major famine is 0.52, and the
probability of both a plague and a famine is 0.15. What
is the probability of neither a famine nor a plague?
0.24
0.288
0.37
0.385
0.76
18. #16 The change in scales makes it hard to compare scores on the
1994 math SAT (mean 470, standard deviation 110) and the
1996 math SAT (mean 500, standard deviation 100). Jane
took the SAT in 1994 and scored 500. Her sister Colleen
took the SAT in 1996 and scored 520. Who did better on the
exam, and how can you tell?
A) Colleen—she scored 20 points higher than Jane.
B) Colleen—her standard score is higher than Jane's.
C) Can't tell from the information given.
D) Jane—the standard deviation was bigger in 1994.
E) Jane—her standard score is higher than Colleen's.
19. #17 The scores on a university examination are normally
distributed with a mean of 62 and a standard deviation
of 11. If the bottom 5% of students will fail the course,
what is the lowest mark that a student can have and still
be awarded passing grade?
A) 57.
B) 62.
C) 40.
D) 44.
E) 43.
20. #18 A study gathers data on the outside temperature during the winter,
in degrees Fahrenheit, and the amount of natural gas a household
consumes, in cubic feet per day. Call the temperature x and gas
consumption y. The house is heated with gas, so x helps explain y.
The least-squares regression line for predicting y from x is
y = 1344 – 19x. On a day when the temperature is 20°F, the
regression line predicts that gas used will be about
1325 cubic feet
1724 cubic feet
964 cubic feet
1383 cubic feet
None of these
21. #19 Suppose we fit the least-squares regression line to a set
of data. If a plot of the residuals shows a curved
pattern,
outliers must be present.
the correlation must be positive.
r2 = 0.
the correlation must be 0.
a straight line is not a good summary for the data.
22. #20 One hundred volunteers who suffer from severe depression are
available for a research study to test the effectiveness of a new
drug in treating severe depression. What is the best method to use
to test the effectiveness of this new drug against the old drug?
Randomly assign volunteers to two groups: one group will take the new drug and the other group takes the old drug.
Randomly choose volunteers and allow them to select which drug they want to take.
Randomly choose volunteers to take the new drug and ask volunteers using the old drug how effective the old drug is.
Randomly assign volunteers to two groups: one group will take the new drug and the other group takes a placebo.
Assign the new drug to the volunteers who are the most severely depressed and assign the old drug to the least depressed volunteers.
23. #21 The following text is a computer printout from regression analysis on a
program called Data Desk. The data compares the temperature of Bismarck,
North Dakota to New York, on randomly selected days.
Variable Coefficient
Constant 23.5915 r2 = 99.0%
Bismarck 0.740767 r2(adj) = 98.9%
Which is the best interpretation of the slope of the regression line?
For each degree increase in Bismarck, the New York temperature increases by 23.5915 degrees.
For each degree increase in New York, the Bismarck temperature increases by 0.740767 degrees.
For each degree increase in Bismarck, the New York temperature increases by 0.740767 degrees.
For each degree increase in New York, the Bismarck temperature increases by 23.5915 degrees.
For each degree increase in New York, the Bismarck temperature increases by .99 degrees.
24. #22 A forester measured 27 of the trees in a large woods that is up
for sale. He found a mean diameter of 10.4 inches and a
standard deviation of 4.7 inches. Suppose that these trees
provide an accurate description of the whole forest and that a
Normal model applies. If a certain tree is at a z = 1.3. What is
the diameter of the tree?
9.1 inches
11.7 inches
16.51 inches
13.52 inches
6.11 inches
25. #23 You are comparing the results of males and females in an
experiment. Which graphical display would you NOT use?
dot plots
Parallel box plots
scatter plot
histogram
Back-to-back stem plots
26. #24 The correlation coefficient measures
whether or not a scatter plot shows an interesting pattern.
the strength of the linear relationship between two quantitative variables.
the strength of the relationship between two quantitative variables.
whether there is a relationship between two variables.
whether a cause and effect relation exists between two variables.
27. #25 If the point in the upper right corner of this
scatter plot is removed from the data, what will
happen to the slope of the line of best fit and
the correlation coefficient?
Both will increase.
Both will decrease.
Slope will increase, r will decrease.
Slope will decrease, r will increase.
Both will remain the same.
28. #26 To check the effect of heat on durability of crack sealant for
Sidewalks, two brands of sealant are used, one brand of economy
sealant and one brand of commercial sealant are tested. Twenty tubes
from the economy sealant are placed in an extremely high temperature
oven for ten hours and twenty tubes from the commercial sealant are
placed at room temperature. The amount of leakage is measured on
each sealant, and the mean for the economy sealant is compared to the
mean for the commercial sealant. Is this a good experimental design?
A. No, because the means are not proper statistics for comparison.
B. No, because more than two brands should be used.
C. No, because more temperatures should be used.
D. No, because temperature is confounded with brand.
E. Yes
29. #27 A survey of 57 students was conducted to determine whether or not
they held jobs outside of school. Of the 57 students, 31 had no job.
Of the Juniors surveyed only 5 had no job.
I. Are the events “Junior” and “no job” independent event?
II. Are the events “Junior” and “no job” disjoint events?
yes; no
no; no
yes; yes
no; yes
Not enough information is given.
30. #28 A company wanted to determine the health care costs of its employees.
A sample of 50 employees were interviewed and their medical expenses
for the previous year were determined. Later the company discovered
that the highest medical expense in the sample was mistakenly recorded
as 25 times the actual amount. However, after correcting the error,
the corrected amount was still greater than or equal to any other medical
expense in the sample. Which of the following sample statistics must
have remained the same after the correction was made?
A. Mean
B. Median
C. Mode
D. Range
E. Variance
31. #29 The equation of the least squares regression
line for the points on the scatter plot above
is . What is the residual for
the point (3, 5)?
A. 1.51
B. 3.00
C. 3.49
D. 5.00
E. 8.49
32. #30 There were 100 rats put through a series of 3 mazes in a lab experiment.
There were 36 rats that ran through maze A, 40 rats ran through maze
B, and 28 rats ran through maze C. Twelve rats ran through both maze
A and B, 15 rats ran through both maze B and C, 10 rats ran through
both maze A and C, and 5 rats ran through all 3 mazes. What is the
probability that a rat did not run through any of the mazes?
16%
23%
28%
40%
72%
33. Answers 1. B 11. D 21. C
2. B 12. C 22. C
3. A 13. A 23. C
4. D 14. A 24. B
5. D 15. E 25. D
6. C 16. E 26. D
7. B 17. D 27. B
8. D 18. C 28. B
9. C 19. E 29. A
10. B 20. A 30. C