1. Ergonomics is the science of making sure that human surroundings are adapted to human needs. How could statistics play a role in the following:
a. Choosing the height of an office chair so that 95 percent of the employees (male and female) will feel it is the "right height" for their legs to reach the floor comfortably.
b. Designing a drill press so its controls can be reached and its forces operated by an "average employee".
c. Defining a doorway width so that a "typical" wheelchair can pass through without coming closer than 6 inches from either side.
d. Setting the width of a parking space to accommodate 95 percent of all vehicles at your local Walmart.
e. Choosing a font size so that a highway sign can be read in daylight at 100 meters by 95 percent of all drivers.
All of these involve taking samples from the population of interest and estimating the value of the variable of interest.
All of these require the designer to take a census of the population who will be using the chair, drill press, doorway, parking space, or highway signs, in order to ensure 100% are accommodated.
All of these product specifications could be determined by a smart engineer or designer who represents the "typical" person using each of the products.
None of the above
2. Which measurement level (nominal, ordinal, interval, ratio) is each of the following variables?
(a) Number of employees in the Walmart store in Hutchinson, Kansas.
(b) Number of merchandise returns on a randomly chosen Monday at a Walmart store.
(c) Temperature (in Fahrenheit) in the ice-cream freezer at a Walmart store.
(d) Name of the cashier at register 3 in a Walmart store.
(e) Manager's rating of the cashier at register 3 in a Walmart store.
(f) Social security number of the cashier at register 3 in a Walmart store.
3. The target population is all stocks in the S&P 500 index. Is each of the following a parameter or a statistic?
(a) The average price/earnings ratio for all 500 stocks in the S&P index.
(b) The proportion of all stocks in the S&P 500 index that had negative earnings last year.
(c) The proportion of energy-related stocks in a random sample of 50 stocks.
(d) The average rate of return for 20 stocks recommended by a broker.
4. A survey of 500 potential customers for new vehicles across the United States indicated that 37 percent expected their next vehicle to be a hybrid.
What kind of sampling method do you suppose was used to arrive at this estimate?
systematic sample
Convenience sample
Cluster sample
Judgment sample
5. A financial magazine publishes an annual list of major stock funds. Last year, the list contained 1,699 funds.
What method would you recommend to obtain a sample of 20 stock funds to estimate the 10-year percent return?
Simple random sample or systematic sampling
Judgment sampling
Cluster sampling or Convenience sampling
6. The target population is all students in your university. You wish to estimate the average current Visa balance for each student. How large would the university student population have to be in order to be regarded as effectively infinite in each of the following samples?
(a) A sample of 9 students.
(b) A sample of 60 students.
(c) A sample of 91 students.
7. The U.S. Postal Service will ship a Priority Mail® Large Flat Rate Box (12" × 12" × 5½") anywhere in the United States for a fixed price, regardless of weight. The weights (ounces) of 20 randomly chosen boxes are shown below.
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72
|
86
|
28
|
67
|
64
|
65
|
45
|
86
|
31
|
32
|
|
39
|
92
|
90
|
91
|
84
|
62
|
80
|
74
|
63
|
86
|
(a) Select the stem-and-leaf diagram.
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Stem and Leaf plot for
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Weights
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stem unit =
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10
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leaf unit =
|
1
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Frequency
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Stem
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Leaf
|
|
1
|
2
|
8
|
|
3
|
3
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1 2 9
|
|
1
|
4
|
5
|
|
0
|
5
|
|
|
5
|
6
|
2 3 4 5 7
|
|
2
|
7
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2 4
|
|
5
|
8
|
0 4 6 6 6
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3
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9
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0 1 2
|
|
20
|
|
|
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Stem and Leaf plot for
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Weights
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stem unit =
|
10
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leaf unit =
|
1
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|
|
|
|
|
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Frequency
|
Stem
|
Leaf
|
|
1
|
2
|
8
|
|
3
|
3
|
1 2 9
|
|
1
|
4
|
5
|
|
0
|
5
|
|
|
5
|
6
|
2 3 4 5 7
|
|
1
|
7
|
4
|
|
4
|
8
|
0 4 6 6
|
|
3
|
9
|
0 1 2
|
|
18
|
|
|
|
Stem and Leaf plot for
|
Weights
|
|
|
stem unit =
|
10
|
|
|
leaf unit =
|
1
|
|
|
|
|
|
|
Frequency
|
Stem
|
Leaf
|
|
1
|
2
|
8
|
|
3
|
3
|
1 2 9
|
|
2
|
4
|
5 5
|
|
2
|
5
|
6 9
|
|
5
|
6
|
2 3 4 5 7
|
|
2
|
7
|
2 4
|
|
3
|
8
|
4 6 6
|
|
2
|
9
|
1 2
|
|
20
|
|
|
(b) Select the correct histogram.
(c) The distribution appears to be
one Modal
No mode
Bimodal