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# Various Statistical Problems

See the attached file.

Problem 2.5
The following information is collected from students upon exiting the campus bookstore during the first week of classes:
a. Amount of time spent shopping in the bookstore
b. Number of textbooks purchased
c. Academic major
d. Gender
Classify each of these variables as categorical or numerical. If the variable is numerical, determine whether the variable is discrete or continuous. In addition, determine the level of measurement for each of these variables.

Problem 2.25
Each day at large hospital, several hundred laboratory tests are performed. Te rate at which these tests are done improperly (and therefore need to be redone) seems steady, at about 4%. In an effort to get the root cause of these nonconformances, tests that need to be redone, the director of the lab decided to keep records over a period of one week. The laboratory tests were subdivided by the shift of workers who performed the lab tests. The results are as follows:
LAB TESTS SHIFT
PERFORMED Day Evening Total

Nonconforming 16 24 40
Conforming 654 306 960
Total 670 330 1,000

a. Construct contingency tables based on total percentages, row percentages, and column percentages.
b. Which type of percentage---row, column, or total---do you think is the most is most informative for these data? Explain.
c. What conclusions concerning the pattern of nonconforming laboratory tests can the laboratory director reach?

Problem 2.35
A manufacturing company produces electric insulators. If the insulators break when in use, a short circuit is likely to occur. To test the strength of the insulators, destructive testing in high-powered labs is carried out to determine how much force is required to break the insulators. Force is measured by observing how many pounds must be applied to insulator before it breaks. Data are collected from sample of 30 insulators. The file Force contains the strengths as follows:

1,870 1,728 1,656 1,610 1,634 1,784 1,522 1,696
1,592 1,662 1,866 1,764 1,734 1,662 1,734 1,774
1,550 1,756 1,762 1,866 1,820 1,744 1,788 1,688
1,810 1,752 1,680 1,810 1,652 1,736

a. Construct a frequency distribution and a percentage distribution.
b. Construct a cumulative percentage distribution.
c. What can you conclude about the strength of the insulators if the company requires a force measurement of at least 1,500 pounds before the insulator breaks?

Problem 2.51
The file DarkChocolate contains the cost per ounce (\$), for a sample of 14 dark chocolate bars.
0.68 0.72 0.92 1.14 1.42 0.94 0.77
0.57 1.51 0.57 0.55 0.86 1.41 0.90
Source: Data extracted from Dark Chocolate: Which Bars Are Best
Consumer Reports, September 2007,p.8.
a. Places the data into an ordered array.
b. Construct a stem-and-leaf display
c. Does the ordered array or the stem-and-leaf display provide more information? Discuss.
d. Around What value, if any, is the cost of dark chocolate bars constructed? Explain?

Problem 3.11
The file Sedans contains the overall miles per gallon
27 31 30 28 27 24 29 32
32 27 26 26 25 26 25 24
Source: Data extracted from Vehicle Rating Consumer Reports, April 2009, p.27.
a. Compute the mean, median, and mode.
b. Compute the variance, standard deviation, range, coefficient of variation, and Z scores.
c. Are the data skewed? Is so, how?
d. Compute the results of (a) through (c) to those of problem3.12 (2) through (c) that refer to the miles per gallon of SUVs priced under \$30,000.

Problem 3.19
General Electric (GE) is one of the world's largest companies; it develops, manufactures, and markets a wide range of products, including medical diagnostic imaging devices, jet engines, lighting products, and chemicals. Through its affiliate, NBC Universal, GE produces and delivers network television and motion pictures. In 2007, GEs stock stock price rose 2.67%, but in 2008, the price dropped 53.94%.
Source: Data extracted from finance.yahoo.com, June 18,2009.
a. Compute the geometric mean rate of increase for the two-year period 2007-2008. (Hint: Denote an increase of 2.67% as R1= 0.027.)
b. If you purchased \$1,000 of GE stock at the start of 2007, what was its value at the end of 2008?

#### Solution Preview

Problem 2.5
The following information is collected from students upon exiting the campus bookstore during the first week of classes:
a. Amount of time spent shopping in the bookstore ( Numerical, Continuous ; Level: Interval scale)
b. Number of textbooks purchased ( Numerical, Discrete-Cannot have 2.5 books; Level: Ratio scale)
c. Academic major (Categorical; Level: Nominal scale-order does not matter)
d. Gender (Categorical; Level: Nominal scale-order does not matter)
Classify each of these variables as categorical or numerical. If the variable is numerical, determine whether the variable is discrete or continuous. In addition, determine the level of measurement for each of these variables.

Answer=See options above)

Problem 2.25
Each day at large hospital, several hundred laboratory tests are performed. Te rate at which these tests are done improperly (and therefore need to be redone) seems steady, at about 4%. In an effort to get the root cause of these nonconformances, tests that need to be redone, the director of the lab decided to keep records over a period of one week. The laboratory tests were subdivided by the shift of workers who performed the lab tests. The results are as follows:
LAB TESTS SHIFT
PERFORMED Day Evening Total

Nonconforming 16 24 40
Conforming 654 306 960
Total 670 330 1,000

a. Construct contingency tables based on total percentages, row percentages, and column percentages.

Row percentages ((count/row total )*100%)
LAB TESTS SHIFT
PERFORMED Day Evening Total

Nonconforming 40(eg, 16/40*100%) 60 100
Conforming 68.13 31.88 100

Column percentages ((count/column total)*100%)
LAB TESTS SHIFT
PERFORMED Day Evening

Nonconforming 2.39(eg, 16/670*100%) 7.27
Conforming 97.61 92.73
Total ...

#### Solution Summary

The solution provides answers to various statistical problems.

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