91影视

The article 鈥淓ffects of Short-Term Warming on Low and High Latitude Forest Ant Communities鈥� (Ecoshpere, May 2011, Article 62) described an experiment in which observations on various characteristics were made using mini chambers of three different types: (1) cooler (PVC

frames covered with shade cloth), (2) control (PVC frames only), and (3) warmer (PVC frames covered with plastic).One of the article鈥檚 authors kindly supplied the accompanying data on the difference between air and soil temperatures(掳C).

Cooler Control Warmer

1.59 1.92 2.57

1.43 2.00 2.60

1.88 2.19 1.93

1.26 1.12 1.58

1.91 1.78 2.30

1.86 1.84 0.84

1.90 2.45 2.65

1.57 2.03 0.12

1.79 1.52 2.74

1.72 0.53 2.53

2.41 1.90 2.13

2.34 2.86

0.83 2.31

1.34 1.91

1.76

a. Compare measures of center for the three different samples.

b. Calculate, interpret, and compare the standard deviations for the three different samples.

c. Do the fourth spreads for the three samples convey the same message as do the standard deviations about relative variability?

d. Construct a comparative boxplot (which was included in the cited article) and comment on any interesting features.

Zinfandel is a popular red wine varietal produced almostexclusively in California. It is rather controversialamong wine connoisseurs because its alcohol contentvaries quite substantially from one producer to another.In May 2013, the author went to the website klwines.com, randomly selected 10 zinfandels from among the 325 available, and obtained the following values of alcoholcontent (%):

14.8 14.5 16.1 14.2 15.9

13.7 16.2 14.6 13.8 15.0

1. Calculate and interpret several measures of center.
2. Calculate the sample variance using the defining formula.
3. Calculate the sample variance using the short cut formula after subtracting 13 from each observation

Exercise 34 presented the following data on endotoxin concentration in settled dust both for a sample of urban homes and for a sample of farm homes:

U: 6.0 5.0 11.0 33.0 4.0 5.0 80.0 18.0 35.0 17.0 23.0

F: 4.0 14.0 11.0 9.0 9.0 8.0 4.0 20.0 5.0 8.9 21.0

9.2 3.0 2.0 0.3

a. Determine the value of the sample standard deviation for each sample, interpret these values, and then contrast variability in the two samples. (Hint:\(\sum {{x_i}} \)= 237.0 for the urban sample and =128.4 for the farm sample, and\(\sum {x_i^2} \)= 10,079 for the urban sample and 1617.94 for the farm sample.)

b. Compute the fourth spread for each sample and compare. Do the fourth spreads convey the same message about variability that the standard deviations do? Explain.

c. Construct a comparative boxplot (as did the cited paper)and compare and contrast the four samples.

A study of the relationship between age and variousvisual functions (such as acuity and depth perception)reported the following observations on the area of sclerallamina (\({\bf{m}}{{\bf{m}}^2}\)) from human optic nerve heads(鈥淢orphometry of Nerve Fiber Bundle Pores in theOptic Nerve Head of the Human,鈥� Experimental EyeResearch, 1988: 559鈥�568):

2.75 2.62 2.74 3.85 2.34 2.74 3.93 4.21 3.88

4.33 3.46 4.52 2.43 3.65 2.78 3.56 3.01

a. Calculate \(\sum {{x_i}} \)and \(\sum {x_i^2} \).

b. Use the values calculated in part (a) to compute the sample variance s2 and then the sample standard deviation s.

a. Give three different examples of concrete populations and three different examples of hypothetical populations.

b. For one each of your concrete and your hypothetical populations, give an example of a probability question and an example of an inferential statistics question.

In 1997 a woman sued a computer keyboard manufacturer,charging that her repetitive stress injuries werecaused by the keyboard (Genessy v. Digital EquipmentCorp.).The injury awarded about \(3.5 million for painand suffering, but the court then set aside that awardas being unreasonable compensation. In making this determination, the court identified a 鈥渘ormative鈥� group of27 similar cases and specified areasonable award as onewithin two standard deviations of the mean of the awardsin the 27 cases. The 27 awards were (in \)1000s) 37, 60,75, 115, 135, 140, 149, 150, 238, 290, 340, 410, 600, 750,750, 750, 1050, 1100, 1139, 1150, 1200, 1200, 1250,1576, 1700, 1825, and 2000, from which\(\sum {{x_i} = } \)20,179,\(\sum {x_i^2} = 24,657,511\). What is the maximum possible amount that could be awarded under the two- standard deviation rule?

The article 鈥淎 Thin-Film Oxygen Uptake Test for the Evaluation of Automotive Crankcase Lubricants鈥� (Lubric. Engr., 1984: 75鈥�83) reportedthe following data on oxidation-induction time (min) for various commercial oils:

87 103 130 160 180 195 132 145 211 105 145

153 152 138 87 99 93 119 129

a. Calculate the sample variance and standard deviation.

b. If the observations were re expressed in hours, what would be the resulting values of the sample variance and sample standard deviation? Answer without actually performing the re expression

The first four deviations from the mean in a sample of n=5 reaction times were .3, .9, 1.0, and 1.3. What is the fifth deviation from the mean? Give a sample for which these are the five deviations from the mean.

A mutual fund is a professionally managed investment scheme that pools money from many investors and invests in a variety of securities. Growth funds focus primarily on increasing the value of investments, whereas blended funds seek a balance between current income and growth. Here is data on the expense ratio (expenses as a % of assets, from www .morningstar.com) for samples of 20 large-cap balanced

funds and 20 large-cap growth funds (鈥渓argecap鈥� refers to the sizes of companies in which the funds invest; the population sizes are 825 and 762,

respectively):

Bl 1.03 1.23 1.10 1.64 1.30

1.27 1.25 0.78 1.05 0.64

0.94 2.86 1.05 0.75 0.09

0.79 1.61 1.26 0.93 0.84

Gr 0.52 1.06 1.26 2.17 1.55

0.99 1.10 1.07 1.81 2.05

0.91 0.79 1.39 0.62 1.52

1.02 1.10 1.78 1.01 1.15

a. Calculate and compare the values of\(\bar x\),\(\tilde x\), and sfor the two types of funds.

b. Construct a comparative boxplot for the two types of funds, and comment on interesting features.

Grip is applied to produce normal surface forces that compress the object being gripped. Examples include two people shaking hands, or a nurse squeezing a patient鈥檚 forearm to stop bleeding. The article 鈥淚nvestigation of Grip Force, Normal Force, Contact Area, Hand Size, and Handle Size for Cylindrical Handles鈥� (Human Factors, 2008: 734鈥�744) included the following data on grip strength (N) for a sample of 42

individuals:

16 18 18 26 33 41 54 56 66 68 87 91 95

98 106 109 111 118 127 127 135 145 147 149 151 168

172 183 189 190 200 210 220 229 230 233 238 244 259

294 329 403

a. Construct a stem-and-leaf display based on repeating each stem value twice, and comment on interesting features.

b. Determine the values of the fourths and the fourth spread.

c. Construct a boxplot based on the five-number summary, and comment on its features.

d. How large or small does an observation have to be to qualify as an outlier? An extreme outlier? Are there any outliers?

e. By how much could the observation 403, currently the largest, be decreased without affecting\({f_s}\)?