Difference between revisions of "Chance News 55"

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6.  Do you agree with the "pretty simple" reason given for the increased rate of bumping?
 
6.  Do you agree with the "pretty simple" reason given for the increased rate of bumping?
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==The Bulgarian Lottery==

Revision as of 21:00, 23 September 2009

Quotations

Populism, in its latest manifestation, celebrates ignorant opinion and undifferentiated rage. .... The typical opinion poll … doesn’t trouble to ask whether the respondent knows the first thing about the topic being opined upon, and no conventional poll disqualifies an answer on the ground of mere total ignorance. The premise of opinion polling is that people are, and of right ought to be, omni-opinionated – that they should have views on all subjects at all times – and that all such views are equally valid. …. So, given the prominence of polls in our political culture, it’s no surprise that people have come to believe that their opinions on the issues of the day need not be fettered by either facts or reflection. …. Now there’s the intellectual free lunch: I’m entitled to vociferous opinions on any subject, without having to know, or even think, about it.

Michael Kinsley, The New Yorker, February 6, 1995

We live in a world of real dangers and imagined fears. …. We are hounded by what I call “psycho-facts”: beliefs that, though not supported by hard evidence, are taken as real because their constant repetition changes the way we experience life. …. We act as if there’s a constitutional right to immortality and that anything that raises risk should be outlawed. ….

Robert J. Samuelson, Newsweek, May 9, 1994

In a September 18 Statesman Journal story, “Ducks’ defense faces tough challenge”, a coach was quoted:

The only statistic that counts is winning and losing …. We don't get caught up in that. .... How many yards and those things.


A retiring associate professor of math at BVU was described in a Storm Lake Pilot Tribune article [1] of September 17:

His love for math outweighed his love of sports by a few percentage points.

Forsooths

Responding to a Canadian viewer who pointed out that "life expectancy in Canada under our health system is higher than the USA," Fox's Bill O'Reilly on 7/27/09 said,

Well, that's to be expected, Peter, because we have 10 times as many people as you do. That translates to 10 times as many accidents, crimes, down the line.


According to a September 18 FOX8 News WVUE-TV story, “Chance for rain”, the following information was published in a cover story in an early 2009 bulletin of the American Meteorological Society:

[Researchers at the University of Washington] found people in Seattle didn't have much of a grasp for what the probability forecast [of rain] really means, but found the numbers helpful in planning their day.


Hanna Karp, in “What’s the Point of Cheerleading?”, The Wall Street Journal, September 17, 2009, states:

Risk-assessment experts say it’s hard to get a handle on the perils of cheerleading.

Breaking News

The Wall Street Journal of September 8, 2009 reports on a study in the Journal of Bone and Joint Surgery: “The researchers compared the outcomes of patients who underwent surgery between 6 a.m. and 4 p.m. for fractures of the femur or tibia to those who had comparable surgeries for similar fractures outside those normal hours.”

Sample

Reoperations

Needed

Sample Size
Sample Proportion
Outside Normal Hours
28
82

.3415

Within Normal Hours
12
70
.1714

The results are:

Difference = p (1) - p (2) Estimate for difference: 0.170035 95% CI for difference: (0.0346494, 0.305420) Test for difference = 0 (vs not = 0): Z = 2.37 P-Value = 0.018

Fisher's exact test: P-Value = 0.026

Discussion

1. Why is the Fisher exact test P-Value (0.026) to be preferred to the other P-Value mentioned (0.018)?

2. The Wall Street Journal mentioned several caveats “making it difficult to determine the underlying reasons for the after-hours patients’ poor outcomes.” List a few practical significance hedges to the statistically significant result.

Contributed by Paul Alper

Amazon River at age 1,000,003 years

“Metrics mania: Are Americans too reliant on numbers?”
by John Yemma, The Christian Science Monitor, September 16, 2009

The author first reminds readers of an old joke:

A guy strikes up a conversation with another guy on a long plane flight to South America. They are over the Amazon.

Guy 1: “Did you know that the Amazon is 1,000,003 years old?”
Guy 2: “Really? How can you be so precise?”

Guy 1: “I was on this same flight three years ago, and a geologist told me the Amazon was a million years old.”

He then discusses the difficulty with “metrics-based management” efforts, but concludes, in a hopeful vein, with a formula and some encouragement:

Metrics + Grain of Salt = Somewhat Useful Information.
Still, even if we can’t trust data absolutely, we can extract meaning. We may not know how old the Amazon really is, but we know one thing for certain: It is three years older than when Guy 1 first flew over it.

A blogger comments [2],

So true. I am an European who has lived in the US for almost 20 years. I am constantly amazed at the ‘number obsession’ that seems to rule all areas of society. It may be because this country is so big, that a common measure can only be found in quantities, not qualities.

Gompertz Law of human mortality

“You’re Likely to Live!”
by “Freakonomics,” The New York Times, September 14, 2009
This very brief article describes the “Gompertz Law of human mortality,” provides some statistics about the different chances of dying at different ages, and refers readers to three websites:
(a) Article with Gompertz Law details and graphs: “Your body wasn’t built to last: a lesson from human mortality rates”, "gravity and levity" blog, July 8, 2009.
(b) Applet that gives life expectancy at user-selected age: “Death Probability Calculator”, undated.
(c) TED video of songs, the first of which relates to aging: “Time is marching on”, March 2007.

Things that go bump

“Bumped Passengers Learn a Cruel Flying Lesson”
by Scott McCartney, The Wall Street Journal, September 17, 2009

This article discusses the recent spike in the rates of passenger-bumping by airlines, despite the increased penalties that the federal government requires the airlines to pay bumped-but-ticketed passengers. Although bumping affects fewer than 2 passengers out of every 10,000, that rate rose by 40% in the second quarter of 2009 over the rate for the second quarter of 2008.

It's pretty simple: It's just because planes are more full than last year," says [a US Airways official, whose airline] had the highest bumping rate among major airlines, at 1.88 passengers per 10,000 in the second quarter.
This summer, the nine major airlines filled 85.5% of their seats, up from 84.1% last summer. The peak was July, with 86.7% of seats filled.

Federal rules allow airlines to overbook in order to compensate for no-shows. The recent increase in bumping rates may be explained by the reduced demand for air travel, especially by business customers.

The [Department of Transportation] says it isn't concerned about the rise in bumping because the rates are still lower than historical highs. During the 1970s and 1980s, bumping rates were routinely four times as high as today's rate.

Discussion

Suppose that, on average, 85% of ticket-holders show up for their flights. Assume that the distribution of the number of ticket-holders who show up is binomial (especially that every ticket-holder has the same chance of being bumped) and that a ticket-holder is bumped only due to lack of a seat.

1. For each n tickets sold, or over-sold, for a 200-seat plane, find the number of ticket-holders an airline could expect to show up, on average.
(a) n = 200 (b) n = 210 (c) n = 220 (d) n = 230 (e) n = 240 (f) n = 250.

2. It appears that the airline would not have to bump any ticket-holders for some values of n. Is that a statistically correct inference, based on your understanding of expected value? Even if those expected values always “came true,” what problem would remain for the airline?

3. For each n tickets sold, or over-sold, find the probability of at least one ticket-holder being bumped off the 200-seat plane.
(a) n = 200 (b) n = 210 (c) n = 220 (d) n = 230 (e) n = 240 (f) n = 250.

4. For which value(s) of n would you have a negligible risk of being bumped? Under what circumstances might any risk be too great?

5. The more tickets an airline sells, the more likely it is to fill the plane and thus maximize its revenue for a flight. However, at some point, the increased revenue may be offset by losses of future dollars from angry ticket-holders and compensation payouts to increasing numbers of bumped ticket-holders. What other information would you want/need to know before deciding how many tickets to sell for a 200-seat plane?

6. Do you agree with the "pretty simple" reason given for the increased rate of bumping?

The Bulgarian Lottery