!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! CHANCE News 3.12 (11 Aug to 1 Sep 1994) !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Prepared by J. Laurie Snell, with help from Jeanne Albert, William Peterson and Fuxing Hou, as part of the CHANCE Course Project supported by the National Science Foundation. Please send comments and suggestions for articles to firstname.lastname@example.org Back issues of Chance News and other materials for teaching a CHANCE course are available from the Chance Web Data Base in the Multimedia Online Document Library at the Geometry Center Mosaic (http:\\geom.umn.edu\) or from their Gopher (geom.umn.edu) in Geometry Center Resources. ======================================= What used to be called prejudice is now called a null hypothesis. A. W. F. Edwards ========================================
OTHER INTERNET SOURCES
Dow Jones historical data
We mentioned the M.I.T. experimental stock market data
last time, that gives the prices of a large number of
stocks, but could not find the historical data for the
Dow Jones averages. Shunhui Zhu informed us that you can
obtain such data by ftp to dg-rtp.dg.com. The directory
We will put the Dow Jones closing values from 1930 to
1992 and the daily Standard and Poor closing values from
1928 to 1987 in the "Teaching Aids" in the Chance Data
FROM OUR READERS
James Hilton suggested the following article:
Breakthroughs: Cranberry Therapy.
Discover Magazine, August 1994, p13
Issue: August, 1994
A study carried out at the Women's Hospital in Boston suggests that women who have a daily cranberry drink are less likely to harbor bacteria that cause urinary tract infections. Since this is a problem mostly for elderly women, researchers studied 153 women whose average age was 78. Each day for six months, half the women drank a ten- ounce glass of cranberry juice while the other half was given a placebo drink with the taste and color of the real thing. At the trial's end, 28 percent of the women taking the placebo had bacteria in their urine. Only 15 percent of those who had the cranberry drink were similarly infected. DISCUSSION QUESTIONS: Is the difference found in this study statistically significant? <<<========<<
>>>>>==========>> Milt Eisner suggested the following DNA article: DNA: What the code won't unlock; in the search for evidence, our faith in science can lead us astray.
Washington Post, 14 August 1994, C3
This is a well-written account of DNA fingerprinting, much of which was covered in articles we have previously abstracted. Here are a couple of points we found interesting. James Starrs, a professor of law and forensic science who has participated in many DNA trials, says that juries are enthralled by color charts and graphs of DNA. He comments: "I've never seen a jury so alert -- no understanding, but alert, following the Yellow Brick Road. I don't know of any other instance in forensics where the jury is just overwhelmed with a visual and pictorial presentation." He remarks that he had a pretty hard time understanding it himself when he attended a seminar on DNA testing. A second interesting observation was: in 1987 Fred Zain, a former DNA technician at West Virginia's criminal laboratory, testified that the semen from a crime scene was that of the defendant. Five years later another DNA test proved this person innocent. An investigation found that Zain had been falsifying DNA results for years, apparently on a misguided one-man crusade against crime. DISCUSSION QUESTION: If the F.B.I testifies that there is a one-in-a-billion chance of a match as good as that found in the evidence, do you think the possibility of a Zain in their organization was taken into account? <<<========<<
>>>>>==========>> DNA Fingerprinting; It's a case of probabilities.
Boston Globe, 22 August, 1994
Another DNA article, well-written, but again covering familiar ground. We found this one interesting because of the quotes from the well know statistician Herman Chernoff. For example, Chernoff says that experts "will quote odds of 1 in 100 billion that a DNA match could have occurred by chance", only to have a lawyer attack them on the grounds that "there are only 5 billion people in the world" - a statistically irrevelant fact. Eric Lander predicts that Simpson's defense attorneys will use a population genetics argument. The very small probabilities are obtained by assuming independence between the alleles at difference positions in the DNA and also between those obtained from mother and father. Both assumptions can be challenged by population genetics. There are ways to give less convincing probabilities for match that do not rely so heavily on these assumptions. The lawyers will argue that the disagreement between what number to quote will show that the evidence does not meet legal standards for use in a trial. The article has an excellent discussion of what the population genetics argument is all about. DISCUSSION QUESTION: Do you agree that the remark that when odds of 1 in 100 billion for a match are given, the fact that there are only 5 billion people in the world is a statistically irrelevant fact? If so why? <<<========<<
Ask Marilyn (A hat check problem).
Parade Magazine, 21 August, 1994
Marilyn Vos Savant
Charles Price is baffled by the following problem: Take an ordinary deck of 52 cards and shuffle it. Then turn the cards over one at a time, counting as you go: ace, two, three, and so on, until you reach king; then start over again. The object is to turn over all 52 cards without having your spoken number match the card in rank that you turn over. Charles mentions that he has tried it hundreds of time and only once turned over all the cards with no match. He expected it to happen more often. Obviously, he wanted to know the chance of getting through the deck without a rank match, but he has to settle for Marilyn telling him only that the expected number of matches is 4 so he should not expect to succeed very often. The origin of matching problems like this and the related "hat check problem" can be found in a book Montmort written in 1708 to help explain some of the common games of the time that involved probability-- in particular, the game of Treise played as follows: One player is chosen as the banker and the others are players. Each player puts up a stake. The banker shuffles the cards and starts dealing calling out the cards in order ace, two, three, ... ,king. The game continues until there is a rank coincidence or the banker has dealt thirteen cards without such a coincidence. If there is no match, the banker pays the players an amount equal to their stakes and a new dealer is chosen. If there is a match he wins from the players an amount equal to their stake and starts a new round counting again ace, two, three, etc. If runs out of cards he reshuffles and continues the count where he left off. Montmort remarks that the dealer has a very favorable game and could easily get several matches before losing the deal. He despairs of finding the actual advantage but solves some related problems. He first simplified the game by assuming that the deck of cards had only 13 cards of one suit. He then found that the probability of getting through the 13 cards without a match was about 1/e = .368 providing the first solution to what is now called the "hat check" problem. Later, with the help of John Bernoulli he showed that in drawing 13 cards from a 52 card deck the chance of not getting a rank match was .357 making it clear that the dealer has a considerable advantage. In the problem that Charles suggested you are to go through the entire deck of 52 cards and this makes the problem harder because you can have different match patterns. Your matches might be with distinct ranks or with the same ranks or both. We called Charles to see where he found the problem and he said that it was a solitaire game that a friend had suggested. Evidently, if you get your letter in Marilyn's column you become an instant celebrity and get lots of phone calls. One of his more interesting calls was from a Steven Landfedler. We called Steven and he told us a story about a lifelong obsession with this problem. He learned this game of solitaire from his grandmother Enrestine Landfelder who was a gypsy from Eastern Europe who played a lot of cards. She called it "frustration solitaire" . Steven was 15 at the time (1956) and tried to find the chance of winning but it was too hard for him. He became obsessed with finding the solution. As he grew older he was better able to read math books but this was certainly not his specialty. He found references that solved the problem but said things like "carrying out "difficult but routine calculations" or, worse yet, mentioned ideas that were a complete mystery to him such as "using Rook Polynomials". (For a solution using the connection to Rook Problems see Riordan's "Introduction to Combinatorial Analysis.") However, Steven persevered and, using what he had gleamed from his reading, was able to work out the solution to his satisfaction. He remarked that he still wanted to find an explanation that he could give to his daughter who is a math teacher. We will try to write up such an explanation. If we succeed we will put on the Chance Data Base in Teaching Aids. (Now who's obsessed with this problem!) DISCUSSION QUESTION: For the game of Treize estimate the expected number of matches before the first run of 13 without a rank match and, from this, estimate the advantage to the banker. <<<========<<
The Price is Right.
Talk given at the summer 1994 MAA meetings.
William T. Butterworth, Barat College, Lake Forest, IL
Paul R. Coe, Rosary College, River Forest IL.
The authors remark that two games "Any Number" and "Spelling Bee" (played on the TV program "The Price is Right") involve interesting probability problems. The "Any Number" game involves trying to guess the numbers in the price of a car before guessing the numbers in either of the prices of two other (lesser) prizes. Each digit 0-9 is used only once among the three prices, and there are initially four unexposed numbers in the price of the car and three in each of the prices of the other two prizes. (The leading 1 in the price of the car is given and does not count as one of the digits.) The contestant guesses one number at a time until all of the digits in the price of one of the prizes have been guessed. The player then wins that prize. The "Spelling Bee" game uses a large board of 30 tiles, on the back of which 11 have a C, 11 have an A, 6 have an R, and 2 have all three letters, C, A, and R. The contestant is allowed to choose from 2 to 5 tiles, the number being based on the contestant's knowledge of the price of several small items. The contestant will win a new car if the word CAR can be spelled using exposed tiles. Additionally, unexposed tiles worth $500 each are revealed sequentially so that the contestant can stop at any time and receive the dollar value of any unexposed tiles. In their talk they showed video clips of the T.V. program and discussed a strategy for stopping in the "Spelling Bee." <<<========<<
>>>>>==========>> Suburban taxes are higher for Blacks. Analysis shows.
The New York Times, 17 August 1994, pg. A1
Diana Jean Schemo
Professor Andrew A. Beveridge of Queens College, in a study for The New York Times of 31 suburbs in the U.S., has found that, in 18 of the suburban regions, or 58 percent, Blacks are taxed higher than Whites on homes of comparable value. The taxes differed by only 3.3 percent, or $38 per year, in suburban Dallas-Fort Worth, but by as much as 47 percent, or $412 per year, near Philadelphia. White homeowners were found to have significantly higher taxes in just one suburb, greater Miami, while in the remaining 12 there was no statistically significant difference. The findings were based on 1990 Census data. The article considers several possible explanations for the apparent disparity, and significant attention is given to questions of intentional versus institutionalized racial discrimination. For the most part, deliberate racism by the taxing jurisdictions or local assessors is downplayed as a likely cause. Rather, it is suggested that recent demographic trends, which have seen the flight of businesses from suburbs where Blacks have moved in and Whites have left, have left a greater tax burden for the newcomers. In addition, to keep their tax burden low, wealthier and more politically organized long-term residents in many traditionally White areas have pressured local governments to delay tax assessments, so that new assessments are more likely to be made only when a house is sold. The article suggests that Blacks have formed a significant proportion of recent suburban home buyers, and have thus been disproportionately taxed at higher rates. DISCUSSION QUESTIONS: 1. Professor Beveridge also examined the tax rates in 30 urban areas and found that Blacks paid higher taxes than Whites on comparable homes in nine cities, or 30 percent, while Whites paid higher taxes in seven cities, or 23 percent. According to the article this analysis was therefore "inconclusive". Why? 2. The Census data on which the study was based came from the responses of Black and White homeowners who were asked: "What is the value of this property; that is, how much do you think this house and lot or condominium unit would sell for if it were for sale? What were the real-estate taxes on this property last year?" The answers to the first question were given in price ranges, to the second in exact dollar amounts. An estimated tax rate for each house was then calculated by dividing the amount of taxes paid by the midpoint of home's price range. The responses of Black and White homeowners in the selected regions were then compared. What do you think of this method of analysis? The article states that the findings were "consistent with those of other researchers who have used sales data..." instead of "subjective estimates". What do you think this remark means? <<<========<<
USA Today, 17 August 1994, pg. 8A
Margaret L. Usdansky
A new study, presented at the meeting of the American Statistical Association in August has found that "almost 10 percent of American men and 6.4 percent of American women have had sex with someone of the same gender at least once in their lives." The article states that these figures are considerably higher than those obtained from other recent studies. The current study, based on a 1988 Louis Harris survey of 1,834 men and women aged 16 to 50, included questions about sexual attraction as well as sexual experiences. According to the article, more than 18 percent of the men and 17 percent of the women had either had sex with or were attracted to a person of their own gender, or both, sometime during their life; but only 4.1 percent of the men and 2.3 percent of the women had exclusively same-sex partners. About 10 percent of the respondents in the survey said they had not had sex with anyone during the past five years. To determine the size of the lesbian and gay population in America, Randall Sell, co-author of the study, points out that: "It all depends on what your definition of homosexuality is." The article also discusses the misconception by many that the population is divided exclusively into two groups, homosexual and heterosexual. Instead, it suggests that there is a broad spectrum of sexual attraction and behavior, and that people may be at different places along the spectrum at different times during their lifes. The article includes the following summary of the study: Sexual experience in the past 5 years (percentages) Men Women Same-sex partners only .8 .3 Same-and-opposite-sex partners 5.4 3.3 Opposite-sex partners only 83.9 86.0 No sexual partners 9.9 10.4 Homosexual experience, attraction since age 15 Men Women Atrractions but no same-sex partners 8.7 11.0 Same-sex partners only rarely 3.6 2.9 Same-sex partners often 1.9 1.2 DISCUSSION QUESTIONS: 1. The study's findings were based on surveys which asked people to describe their sexual feelings and experiences. How reliable do you think this information can be? Would you be completely truthful in responding to such questions? Do you think different responses would be obtained if the questions were asked over the phone as opposed to in writing? How about in person? 2. The opening sentence of the article states that "almost 10 percent of American men and 6.4 percent of American women have had sex with someone of the same gender at least once in their lives." The 10 and 6.4 percent figures are later in the article given as the percentages of the survey respondents who have had these experiences. Why is it possible to extend these percentages to the whole population? <<<========<<
>>>>>==========>> A minority of one percent: the truth about homosexuals.
British Daily Mail, 20 August, p 12
This article begins: "An American study has confirmed British findings that only one percent of men are active homosexuals-- demolishing the long-standing myth of 10 percent." By "active homosexuals", the article is in fact referring to those participants who said they had had a sexual relationship with a member of the same sex, but not with the opposite sex, in the past five years. Acording to the article, the study reported that 1 percent of men and 1/3 percent of women were in this category, which "flatly contradict[s] the estimate of 10 percent for men and women by researcher Alfred Kinsey", who reported his findings forty years ago. The article also states that "between 8 and 12 percent of men and women had homosexual fantasies but never acted them out." These figures agree with those given in the USA today article, but they are not emphasized there. Instead, the USA Today states that "More than 18 percent of men and over 17 percent of women said they had either had sex with someone of the of the same gender or had felt attracted to someone of the same gender - or both". These last figures are also stated in "Men, women in 3 lands polled on homosexual attraction" from The Buffalo News, 24 August 1994, which also says that "the study found homosexuality is far more prevalent than the standard 10 percent attributed to Alfred Kinsey". DISCUSSION QUESTION: The Daily Mail says the study "demolishes" the 10 percent figure, while The Buffalo News says the study found that homosexuality is "far more prevalent" than 10 percent. Why do you think the two papers disagree? How would you define "active homosexual"? The quote from the USA today article "More than 18 percent ...." is correct but does not seem consistent with their table. Can you explain why this might be the case? <<<========<<
Taking vitamins. Can they prevent disease?
CONSUMER REPORTS, September 1994, 561-569.
This article begins by describing the "Great Vitamin Scare of 1994" which resulted after the report of a study from the National Cancer Institute on the effect of beta-carotene supplements on 29,000 male smokers in Finland. This study showed that the incidence of lung cancer was 18% higher in the group of smokers who took beta-carotene supplements than the group of smokers who did not take the supplements. This contradicted more than a dozen population studies showing that people who ate foods rich in beta-carotene had a relatively low lung cancer risk. The NCI study also contradicted previous studies on the benefits of taking vitamin E. The article goes on to describe the aftermath of the study and presents a nice summary of the types of controlled clinical trials used to study the effect of vitamins. Results of studies on diet, antioxidants, and disease (cancer and heart disease) are also summarized. There is a description of current clinical trials which should yield information in the next five years on results of taking vitamin supplements. The authors conclude that it is better to eat more fruits and vegetables than to rely on vitamin supplements to prevent disease. Following the article are tables of data resulting from the Consumer Guide's test of 86 different supplement products: Vitamins C and E, beta-carotene, and multi- vitamin/mineral formulas. The data sets listed include the cost, number of pills per bottle, and manufacturer for each product. DISCUSSION QUESTIONS: 1. What is your opinion of the effect of taking vitamins? Does this article convince you that it is better to eat more fruits and vegetables than to take vitamin supplements? 2. Try to design some other research studies that would better determine the effect of taking vitamins on preventing different diseases. <<<========<<
There are several letters about the study reported in the April 14 issue of this journal which was a controlled study to see if vitamin E and beta carotene supplements could help prevent lung cancer in smokers. See Chance News. The first writes: "What was not comprehensible, and was quite disturbing, was the irresponsible manner in which the findings of the study were interpreted by its authors and those of the accompanying editorial." The writer feels that, since the negative effect of beta- carotene was significant at the 95% level, the authors should have been more forthright about accepting this as a real finding and not just sort of dismissing it as something that probably happened by chance (since previous observational studies suggested that beta carotene was effective). The authors of the original article argue in response that this writer is going too far in thinking that a single study ever settles anything. Other letter-writers express ideas of what might have gone wrong as well as explanations for the apparent negative effect. For example, one writer observes that animal studies have suggested that alcohol interacts with beta carotene to produce negative effects. The writer suggests that, since smokers are known to drink more than others, it may be that this interaction caused the negative effect, at least in part. DISCUSSION QUESTIONS The authors of the editorial that accompanied the original study say: One reason they did not take the negative effect too seriously is that they regard the observation as hypothesis-generating, not hypothesis- testing. The reason they give for this is, the original article had as its hypothesis that beta-carotene had a positive effect. What do they mean by this and do you agree with them? <<<========<<
>>>>>==========>> Beer makes for more trouble than wine.
The Herald(Glasgow), 24 August 1994, p4.
A study on crime and alcohol consumption conducted by Jan van Dyk, professor of criminology at Leyden University in the Netherlands, found that beer-drinking nations have higher levels of assaults and domestic violence than those countries that prefer wine. The study was based on surveys in more than 40 countries. Countries with high levels of beer drinking ranking high in violence included the Netherlands, Britain, Canada and Australia. Countries with high levels of wine drinking, Italy, Greece, Spain and France, had the lowest violence levels. Van Dyk attributes the association to cultural norms, stating that drinking beer and getting into fights are part of "normal recreation patterns" in beer drinking countries. He recommends that the rest of the world follow the lead of Scandinavian countries, which heavily tax alcohol. DISCUSSION QUESTIONS: (1) How does the evidence presented make a case for taxation? Should beer be taxed but not wine? How about taxing beer more heavily? (2) What are some confounding factors for this observational study? <<<========<<
>>>>>==========>> The tyranny of the mean: gender and expectations.
Notices of the AMS, Sept. 1994, pp. 766-769.
Marcia C. Linn
The "tyranny of the mean" refers to people's tendency to rely on expectations about groups rather than about individual performance when evaluating professionals, job applicants, or students. Linn's lead-in example concerns the medical field: since more men are surgeons people expect male surgeons to be better than female surgeons, and will choose a male over a female without considering these individuals' records. She argues that, if anything, the opposite tends to be true: groups with smaller memberships are likely to be more selective. She draws an analogy with the "Gambler's Fallacy," whereby people expect that black is more likely after a run of three reds. Thus expectations for the next spin are confused with expectations for the population distribution of red and black. Linn explains that she was discouraged from studying statistics by advisers who argued that few women went into such fields, thereby applying population expectations to her as an individual. While men score better than women on college entrance math exams, women earn higher grades in pre-college math and science courses. Reasoning from the population expectation leads people to conclude that the exam scores must be better predictors of success in math and science. This is the tyranny of the mean: "test score data supports expectations about success in mathematics based on group membership." But, Linn argues more women would be admitted, and more scholarships awarded to them, if the grades were used as a measure. Having found that women do better in college courses than men with comparable S.A.T. scores, M.I.T. a few years ago relaxed the requirement that students score 750 or higher on the SAT-M. More women were admitted and the gap between women and men's grades decreased and there was a general increase in the overall talent in the class. The article includes a bar chart that compares the performance of men and women in all types of college mathematics courses. From this chart we find Course Number Percent Ave Scores Female Males Females Calculus (Several Universities) 561 29 2.30 2.77 Honors Calculus 173 26 3.22 3.38 Courses beyond Calculus 503 23 2.72 3.00 Calculus 4647 35 2.36 2.41 Pre-calculus 3530 41 2.17 2.38 Regular Math 900 60 2.19 2.52 Remedial Math 2391 48 2.42 2.36 Algebra and Trigonometry 358 39 2.18 2.59 College Algebra 336 52 1.98 2.24 These were taken from a variety of different studies listed in the article. The men picked a poor choice for their single victory over the women. DISCUSSION QUESTIONS 1. Two of the differences between men and women are marked by footnotes "difference tested and not found significant." One is marked "difference tested and found significant. Which do you think these are? What do you think about the other six? 2. Would it be reasonable to combine all the data to do a "meta-analysis" to test the hypothesis that women do better than men in college mathematics courses? 2. In College algebra--marked "not significant"--the bar for the average female grade appears to be 50% longer than that for average male grade, and so visually appears to be one of the most striking differences. What is going on here? 3. Is the author's explanation of the gambler's paradox reasonable? <<<========<<
>>>>>==========>> Gender gap continues to close on S.A.T.'s.
New York Times, 25 August, 1994, A12
The annual report on S.A.T. scores was released by the College Board. The president of the board said: "Since 1987, women have narrowed the male-female gaps in S.A.T. scores by six points for math and verbal, even though they are the majority of S.A.T. takers and come from families with less income and education than men -- factors which tend to depress scores." . The 1994 scores for the A.C.T., or American College Testing, showed that women's scores improved for the third consecutive year, while men's scores dropped. The men's average score on this test is only slightly higher than the female score. It is suggested that the smaller difference between men and women on this test is because it is only about a quarter mathematics, and it is on the mathematics part of the S.A.T. where the large difference occurs. The article includes a table of scores for men and women of different ethnic groups. DISCUSSION QUESTION: Do you think that the president of the board put too positive a spin on his remarks? <<<========<<
>>>>>==========>> Darts trounce professionals in latest duel.
Wall Street Journal, 18 August, 1994, C1
John R. Dorfman
In the continuing contest between the darts and the professionals, the professionals' stocks had an average loss of 10% from Feb. 2 through July 31, while the darts had an average gain of 16.9% in this period. The Dow Jones was down 5.3% in this period. In the series of 50 overlapping six-month contests that were started in 1990, the investment professionals and the Dow Jones are even, at 25 wins each, but the professionals are beating the darts 29-21. DISCUSSION QUESTION How would you decide if the professionals are doing significantly better than the darts? Are they? <<<========<<
Fifteen years ago New York State passed a "truth in testing law" that required the Educational Testing Service to release some of their tests with answers. (We can't seem to find out exactly what information they have to release). Now the author of this legislation is trying to extend it to include computer adaptive tests (CAT). In CAT tests, the student answers a randomly chosen question of medium difficulty and then the computer produces an easier or harder question depending on how good the answer to the previous question was. Such tests are claimed to provide the same information with about half the number of questions used in a more standard test. CAT versions of the graduate record exam have been taken by about 18,000 students, and it is expected to completely replace the pencil and paper version by 1996-7. Under the proposed bill, testing agencies would be required to disclose the item pools that were used in the previous year, along with the correct answers and rules used to determine test scores. Also, during four four-week periods, during each year, examinees would be allowed, immediately after completing a test, to review all the questions they were given, along with the answers. The GRE board wants to release complete copies only once every three years to prevent the pool of questions from being compromised. ETS researchers presented a paper in April, at the annual meeting of the National Council on Measurement in Education, saying that there were a number of unresolved questions: the effect of allowing students to review their questions during a test, the effect of repeated administrations of the test on their validity, how students with little computer expertise will be affected? etc. DISCUSSION QUESTION The article states that ETS has demonstrated in a limited study that scores for a CAT version of the GRE's General Test are "adequately comparable" with scores from a paper-and-pencil form, or can be made so. How do you think they did this study? <<<========<<
>>>>>==========>> What is a 5.8 really? Ranking figure skaters
Canada News Wire, 18 August 1994
This article discusses a study on the methods used in scoring and rating figure skaters that was presented at the recent American Statistical Association meetings in Toronto. A "greatly simplified" description of the process is given: Each skater is first ranked by each judge, and the winner is the one with the highest median rank. Although there is typically an international panel of judges with widely differing backgrounds, according to the article "they are amazingly similar in their scoring." For example, after analyzing two years of competition data, the standard deviation of approximately 700 scores given to men skaters on technical merit was .126. DISCUSSION QUESTIONS: (1) Why do you think the median rank is used, and not the mean? (2) The only talks at the American Statistical Association that were reported on in the media were talks that involved sports or sexuality. Do you find this surprising? !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! CHANCE News 3.12 (11 Aug to 1 Sep 1994) !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Please send suggestions to: email@example.com >>>==========>>|<<==========<<<