ISE 261 HOMEWORK ONE Due Date: Monday 6/02
1. The amount of flow through a solenoid valve in an automobile’s pollution-control system is an important characteristic. An experiment was carried out to study how flow rate depended on five factors: ambient temperature, armature length, spring load, bobbin depth and atmosphere pressure. Four different levels (low, mid-low, mid-high, and high) of each factor were chosen, and a single observation on flow was made for each combination of levels. The resulting data set consisted of how many observations?
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2. The following data represent the length of life in years, measured to the nearest tenth, of 42 similar fuel pumps:
2.0 3.0 0.3 3.3 1.3 0.4 1.5 4.0 5.9 5.8 4.7 0.7 1.0 6.0
0.2 6.0 6.6 6.5 0.8 2.3 4.5 0.9 1.5 0.5 2.5 5.0 5.6 6.0
1.2 0.2 6.7 6.9 1.7 2.1 4.8 5.9 6.1 5.2 6.2 6.3 0.9 6.8
Construct a stem-and-leaf plot for the life in years of the fuel pump using the digit to the left of the decimal point as the stem for each observation.
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3. Compute the sample mean, sample range, and sample standard deviation for the fuel pump data in problem #2.
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4. In a certain company, every worker receives a 12% increase in pay. How does this affect the mean salary of this company? The standard deviation of the company salaries?
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5. An article in the Journal of Transportation Engineering lists the following values of fracture stress (in mega-pascals) measured for a sample of 22 mixtures of hot-mixed asphalt (HMA).
30 75 79 80 90 105 126 138 149 179 190
228 232 236 240 242 245 247 268 290 390 475
Compute the mean, median, and the 5% and 10% trimmed means.
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6. An exoplanet is a planet beyond the Solar System, orbiting around another star. On October 19th, 2009, European astronomers announced their discovery of 32 new planets beyond our solar system. This detection pushes the number of known exoplanets past 400. Over 350 exoplanets are listed in the Extra-solar Planets Encyclopedia. The vast majority have been detected through radial velocity observations and other indirect methods rather than actual imaging. The European astronomers discovered their planets with the High Accuracy Radial Velocity Planet Searcher (HARPS), a spectrograph attached to the European Southern Observatory’s 3.6 –meter telescope in Chile. The spectrograph measures small changes in a star’s radial velocity caused by the gentle gravitational pull from an orbiting planet. A text file on this web page lists the orbital periods (in days) for a sample of these exoplanets. Construct a Histogram from the data available on the text file. You may use a software package (MATLAB (see Hist command), Excel, Mathematica, etc) to assist in development of your Histogram. Remember to label each axis & title your Histogram. Also, you should offer observations of shape.
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7. Coal-fired power plants used in the electrical industry have gained public attention because of the environmental problems associated with solid wastes generated by large-scale combustion. A study was conducted to measure the EC50 (Effective Concentration, in mg/L, that decreases 50% of the light in a luminescence bioassay) at four different locations. The experimental data found:
Largest value = 3,400 Smallest value = 3,300
Sample mean = 3,350 s = 41.80111641
Find the values of the 2-middle sample observations. (Do not use successive guessing).
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8. An article in American Antiquity discusses the strength of ancient ceramics. Several specimens of each of three types of ceramic were tested. The loads (in kg) required to crack the specimens are listed below. Construct comparative boxplots (placed side by side) for the three samples and comment on the features of the three samples.
Ceramic Type Loads (kg)
Sacaton > 15, 30, 51, 20, 17, 19, 20, 32, 17, 15, 23, 19, 15, 18, 16, 22, 29, 15, 13, 15
Gila Plain> 27, 18, 28, 25, 55, 21, 18, 34, 23, 30, 20, 30, 31, 25, 28, 26, 17, 19, 16, 24,
19, 9, 31, 19, 27, 20, 43, 15
Cas Grande> 20, 16, 20, 36, 27, 35, 66, 15, 18, 24, 21, 30, 20, 24, 23, 21, 13, 21
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9. Find the Interquartile Range (IQR) for the two data sets shown below.
Find the first and third quartiles of the asphalt data in problem #5.
A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12,13,14,15,16}
B = {1, 2, 3, 4, 5, 6, 7, 8, 10, 12}
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10. In the following list is the number of hazardous waste sites in each of the 50 US states. The list has been sorted into numerical order. Construct a histogram for these data. Comment on the features.
1 2 3 4 4 5 6 8 8 9
10 10 10 11 11 11 12 12 12 12
13 13 14 15 16 17 17 18 18 19
19 20 22 23 24 25 29 30 33 37
38 39 40 55 58 77 81 96 102 107