STATISTICS
SECTION I
Time – 1 hour and 30 minutes
Number of questions – 40
Percent of total grade – 50
Directions
:
Solve each of the following problems, using the available space for scratch work.
Decide which
is the best of the choices given and fill in the corresponding oval on the answer sheet.
No credit will be
given for anything written in the test book.
Do not spend too much time on any one problem.
1.
The statistics below provide a summary of the distribution of heights, in inches, for a simple random
sample of 200 young children.
Mean:
46 inches
Median:
45 inches
Standard Deviation:
3 inches
First Quartile:
43 inches
Second Quartile:
48 inches
About 100 children in the sample have heights that are
(a) less than 43 inches
(b) less than 48 inches
(c) between 43 and 48 inches
(d) between 40 and 52 inches
(e) more than 46 inches
2.
In which of the following situations would it be most difficult to use a census?
(a) To determine what proportion of licensed bicycles on a university campus have lights.
(b) To determine what proportion of students in a high school support wearing uniforms.
(c) To determine what proportion of registered students enrolled in a college are employed more than 20
hours each week.
(d) To determine what proportion of singlefamily dwellings in a small town have twocar garages.
(e) To determine what proportion of fish in Lake Michigan are bass.
3.
The distribution of the diameters of a particular variety of oranges is approximately normal with a
standard deviation of 0.3 inch.
How does the diameter of an orange at the 67
th
percentile compare with the
mean diameter?
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4.
Independent random samples of 100 luxury cars and 250 nonluxury cars in a certain city are examined to
see if they have bumper stickers.
Of the 250 nonluxury cars, 125 have bumper stickers and of the 100
luxury cars, 30 have bumper stickers.
Which of the following is a 90 percent confidence interval for the
difference in the proportion of nonluxury cars with bumper stickers and the proportion of luxury cars with
bumper stickers from the populations of cars represented by these samples?
7
.
0
3
.
0
250
5
.
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5
.
0
645
.
1
3
.
0
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.
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7
.
0
3
.
0
250
5
.
0
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.
0
96
.
1
3
.
0
5
.
0
+
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+
±

100
1
250
1
350
195
350
155
645
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1
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5
.
0
+
±

100
1
250
1
350
195
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155
96
.
1
3
.
0
5
.
0
(
29
(
29 (
29
+
±

100
1
250
1
6
.
0
4
.
0
645
.
1
3
.
0
5
.
0
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