2.2 Redes de Pares (Peer to Peer)
2.2.5 Arquitecturas Actuales
ogy (Vol. 43, 1995) reported on a study of the
diets and water requirements of spinifex pigeons. Sixteen pigeons were captured in the desert and the crop (i.e., stomach) contents of each examined. The accompanying table reports the weight (in grams) of dry seed in the crop of each pigeon. Use the SAS printout below to find a 99% confidence interval for the average weight of dry seeds in the crops of spinifex pigeons inhabiting the Western Australian desert. Interpret the result.
PIGEONS
.457 3.751 .238 2.967 2.509 1.384 1.454 .818 .335 1.436 1.603 1.309 .201 .530 2.144 .834
Source: Table 2 from Williams, J. B., Bradshaw, D.,
and Schmidt, L. ‘‘Field metabolism and water require- ments of spinifex pigeons (Geophaps plumifera) in Western Australia. ‘‘Australian Journal of Zoology, Vol. 43, no. 1, 1995, p. 7. Reprinted by permission of CSIRO Publishing. http://www.publish.csiro.au/nid/ 90/paper/ZO9950001.htm.
1.100. Psychological stress in victims of violence. Inter- personal violence (e.g., rape) generally leads to psychological stress for the victim. Clinical Psy-
chology Review (Vol. 15, 1995) reported on the
results of all recently published studies of the relationship between interpersonal violence and psychological stress. The distribution of the time elapsed between the violent incident and the ini- tial sign of stress has a mean of 5.1 years and a standard deviation of 6.1 years. Consider a
random sample of n= 150 victims of interper- sonal violence. Let ¯y represent the mean time elapsed between the violent act and the first sign of stress for the sampled victims.
(a) Give the mean and standard deviation of the sampling distribution of ¯y.
(b) Will the sampling distribution of ¯y be approx- imately normal? Explain.
(c) Find P (¯y > 5.5). (d) Find P (4 < ¯y < 5).
1.101. Workers exposed to dioxin. The Occupational Safety and Health Administration (OSHA) con- ducted a study to evaluate the level of exposure of workers to the dioxin TCDD. The distribution of TCDD levels in parts per trillion (ppt) of production workers at a Newark, New Jersey, chemical plant had a mean of 293 ppt and a standard deviation of 847 ppt (Chemosphere, Vol. 20, 1990). A graph of the distribution is shown here. In a random sample of n= 50 workers selected at the New Jersey plant, let ¯y represent the sample mean TCDD level.
0 .10 .20 500 1,000 1,500 2,000 TCDD level (ppt) Relativ e frequency
(a) Find the mean and standard deviation of the sampling distribution of ¯y.
(b) Draw a sketch of the sampling distribution of ¯y. Locate the mean on the graph.
(c) Find the probability that¯y exceeds 550 ppt. 1.102. Alkalinity levels in river water. The mean alka-
linity level of water specimens collected from the Han River in Seoul, Korea, is 50 milligrams per liter (Environmental Science and Engineering, Septem- ber 1, 2000). Consider a random sample of 100 water specimens collected from a tributary of the Han River. Suppose the mean and standard deviation of the alkalinity levels for the sample are¯y = 67.8 mpl and s= 14.4 mpl. Is there sufficient evidence (at
α= .01) to indicate that the population mean
alkalinity level of water in the tributary exceeds 50 mpl?
1.103. Temperature of molten iron. The Cleveland Cast- ing Plant produces iron automotive castings for Ford Motor Company. When the process is stable, the target pouring temperature of the molten iron
is 2,550 degrees (Quality Engineering, Vol. 7, 1995). The pouring temperatures (in degrees Fahrenheit) for a random sample of 10 crankshafts produced at the plant are listed in the table below. Conduct a test to determine whether the true mean pouring temperature differs from the target setting. Test using α= .01.
IRONTEMP
2,543 2,541 2,544 2,620 2,560 2,559 2,562 2,553 2,552 2,553
Source: Price, B., and Barth, B. ‘‘A structural model
relating process inputs and final product characteris- tics,’’ Quality Engineering, Vol. 7, No. 4, 1995, p. 696 (Table 2).
1.104. Mating habits of snails. Genetical Research (June 1995) published a study of the mating habits of hermaphroditic snails. The mating habits of the snails were identified as either self-fertilizing or cross-fertilizing. The effective population sizes of the two groups were compared. The data for the study are summarized in the table. Geneticists are interested in comparing the variation in population size of the two types of mating systems. Con- duct this analysis for the researcher. Interpret the result.
EFFECTIVE POPULATION SIZE SNAIL SAMPLE STANDARD MATING SYSTEM SIZE MEAN DEVIATION
Cross-fertilizing 17 4,894 1,932 Self-fertilizing 5 4,133 1,890
Source: Jarne, P. ‘‘Mating system, bottlenecks, and
genetic polymorphism in hermaphroditic animals.”
Genetics Research, Vol. 65, No. 3, June 1995, p. 197
(Table 4). 2009© Cambridge Journals, reproduced with permission.
1.105. Heights of children who repeat grades. Are chil- dren who repeat a grade in elementary school shorter on average than their peers? To answer this question, researchers compared the heights of Australian schoolchildren who repeated a grade to those who did not (Archives of Disease in Child-
hood, April 2000). All height measurements were
standardized using z-scores. A summary of the results, by gender, is shown in the table on p. 77. (a) Conduct a test of hypothesis to determine
whether the average height of Australian boys who repeated a grade is less than the average height of boys who never repeated. Use α= .05. (b) Repeat part a for Australian girls.
(c) Summarize the results of the hypothesis tests in the words of the problem.
Summary table for Exercise 1.105
NEVER REPEATED REPEATED A GRADE
Boys n= 1,349 n= 86 ¯x = .30 ¯x = −.04 s= .97 s= 1.17 Girls n= 1,366 n= 43 ¯x = .22 ¯x = .26 s= 1.04 s= .94
Source: Reproduced from Archives of Disease in Child- hood, ‘‘Does height influence progression through pri-
mary school grades?” Melissa Wake, David Coghlan, and Kylie Hesketh, Vol. 82, Issue 4, April 2000 (Table 3), with permission from BMJ Publishing Group Ltd.
1.106. College students attitudes toward parents. Researchers at the University of South Alabama compared the attitudes of male college students toward their fathers with their attitudes toward their mothers (Journal of Genetic Psychology, March 1998). Each of a sample of 13 males was asked to complete the following statement about each of their parents: My relationship with my father (mother) can best be described as: (1) awful, (2) poor, (3) average, (4) good, or (5) great. The following data were obtained:
FMATTITUDES
STUDENT ATTITUDE ATTITUDE TOWARD FATHER TOWARD MOTHER
1 2 3 2 5 5 3 4 3 4 4 5 5 3 4 6 5 4 7 4 5 8 2 4 9 4 5 10 5 4 11 4 5 12 5 4 13 3 3
Source: Adapted from Vitulli, W. F., and Richard-
son, D. K. ‘‘College student’s attitudes toward relation- ships with parents: A five-year comparative analysis,’’
Journal of Genetic Psychology, Vol. 159, No. 1 (March
1998), pp. 45–52.
(a) Specify the appropriate hypotheses for testing whether male students’ attitudes toward their fathers differ from their attitudes toward their mothers, on average.
(b) Conduct the test of part a at α= .05. Interpret the results in the context of the problem. 1.107. Mathematics and gender. On average, do males
outperform females in mathematics? To answerthis
question, psychologists at the University of Min- nesota compared the scores of male and female eighth-grade students who took a basic skills math- ematics achievement test (American Educational
Research Journal, Fall 1998). One form of the
test consisted of 68 multiple-choice questions. A summary of the test scores is displayed in the table.
MALES FEMALES
Sample size 1,764 1,739
Mean 48.9 48.4
Standard deviation 12.96 11.85
Source: Bielinski, J., and Davison, M. L. ‘‘Gender differ-
ences by item difficulty interactions in multiple-choice mathematics items,’’ American Educational Research
Journal, Vol. 35, No. 3, Fall 1998, p. 464 (Table 1).
Reprinted by Permission of SAGE Publications.
(a) Is there evidence of a difference between the true mean mathematics test scores of male and female eighth-graders?
(b) Use a 90% confidence interval to estimate the true difference in mean test scores between males and females. Does the confidence inter- val support the result of the test you conducted in part a?
(c) What assumptions about the distributions of the populations of test scores are necessary to ensure the validity of the inferences you made in parts a and b?
(d) What is the observed significance level of the test you conducted in part a?
(e) The researchers hypothesized that the distribu- tion of test scores for males is more variable than the distribution for females. Test this claim at α= .05.
1.108. Visual search study. When searching for an item (e.g., a roadside traffic sign, a lost earring, or a tumor in a mammogram), common sense dic- tates that you will not reexamine items previously rejected. However, researchers at Harvard Medical School found that a visual search has no memory (Nature, August 6, 1998). In their experiment, nine subjects searched for the letter ‘‘T’’ mixed among several letters ‘‘L.’’ Each subject conducted the search under two conditions: random and static. In the random condition, the location of the let- ters were changed every 111 milliseconds; in the static condition, the location of the letters remained unchanged. In each trial, the reaction time (i.e., the amount of time it took the subject to locate the target letter) was recorded in milliseconds.
(a) One goal of the research is to compare the mean reaction times of subjects in the two experimen- tal conditions. Explain why the data should be analyzed as a paired-difference experiment.
(b) If a visual search has no memory, then the main reaction times in the two conditions will not differ. Specify H0 and Ha for testing the ‘‘no memory’’ theory.
(c) The test statistic was calculated as t= 1.52 with
p-value= .15. Make the appropriate conclu- sion.
MILK
1.109. Detection of rigged school milk prices. Each year, the state of Kentucky invites bids from dairies to supply half-pint containers of fluid milk products for its school districts. In several school districts in northern Kentucky (called the ‘‘tri-county’’ market), two suppliers—Meyer Dairy and Trauth Dairy—were accused of price-fixing, that is, con- spiring to allocate the districts so that the winning bidder was predetermined and the price per pint was set above the competitive price. These two dairies were the only two bidders on the milk contracts in the ‘‘tri-county market’’ between 1983 and 1991. (In contrast, a large number of dif- ferent dairies won the milk contracts for school districts in the remainder of the northern Ken- tucky market—called the ‘‘surrounding’’ market.) Did Meyer and Trauth conspire to rig their bids in the tri-county market? If so, economic theory
MINITAB Output for Exercise 1.109(a)
MINITAB Output for Exercise 1.109(b)
states that the mean winning price in the rigged tri- county market will be higher than the mean winning price in the competitive surrounding market. Data on all bids received from the dairies competing for the milk contracts between 1983 and 1991 are saved in the MILK file.
(a) A MINITAB printout of the comparison of mean bid prices for whole white milk for the two Kentucky milk markets is shown below. Is there support for the claim that the dairies in the tri-county market participated in collusive practices? Explain in detail.
(b) In competitive sealed bid markets, vendors do not share information about their bids. Consequently, more dispersion or variability among the bids is typically observed than in collusive markets, where vendors communicate about their bids and have a tendency to submit bids in close proximity to one another in an attempt to make the bidding appear compet- itive. If collusion exists in the tri-county milk market, the variation in winning bid prices in the surrounding (‘‘competitive’’) market will be significantly larger than the corre- sponding variation in the tri-county (‘‘rigged’’) market. A MINITAB analysis of the whole white milk data in the MILK file yielded the
printout at the bottom of p. 78. Is there evidence that the bid price variance for the surrounding market exceeds the bid price variance for the tri-county market?
1.110. Alzheimer’s and homophone spelling. A homo-
phone is a word whose pronunciation is the same
as that of another word having a different meaning and spelling (e.g., nun and none, doe and dough, etc.). Brain and Language (April 1995) reported on a study of homophone spelling in patients with Alzheimer’s disease. Twenty Alzheimer’s patients were asked to spell 24 homophone pairs given in random order, then the number of homo- phone confusions (e.g., spelling doe given the context, bake bread dough) was recorded for each patient. One year later, the same test was given to the same patients. The data for the study are provided in the table. The researchers posed the following question: ‘‘Do Alzheimer’s patients show a significant increase in mean homophone
confusion errors over time?’’ Perform an analysis of the data to answer the researchers’ question. Use the relevant information in the SAS printout. What assumptions are necessary for the procedure used to be valid? Are they satisfied?
HOMOPHONE
PATIENT TIME 1 TIME 2
1 5 5 2 1 3 3 0 0 4 1 1 5 0 1 6 2 1 7 5 6 8 1 2 9 0 9 10 5 8 11 7 10 12 0 3 13 3 9 14 5 8 15 7 12 16 10 16 17 5 5 18 6 3 19 9 6 20 11 8
Source: Neils, J., Roeltgen, D. P., and Constantinidou, F.
‘‘Decline in homophone spelling associated with loss of semantic influence on spelling in Alzheimer’s dis- ease,’’ Brain and Language, Vol. 49, No. 1, Apr. 1995, p. 36 (Table 3). Copyright© 1995, with permission from Elsevier.
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