Probability and Statistics
Probability and Statistics MATH 1530
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Immanuel Turcotte DDS
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Date Created: 10/28/15
BINOMIAL EXPERIMENTS Fixed number of trials n Independent trials Two possible outcomes each trial S success F failure Examples Probabilities remain constant each trial bP N Which of the following can be treated as a binomial experiment Surveying 1000 voters to determine their preference for the next president Surveying 1000 voters to determine whether they would vote in the incumbent Sampling 500 prisoners to determine whether they have been in prison before Sampling 500 prisoners to determine the lengths of their current sentences Testing 300 drivers to determine whether their blood alcohol content levels are more than 010 rug96x p PS probability of success in w trial H03 x of successes in n trials Binomial Probability Formula Px quotCx P qH Px Probability ofx successes in n trials x quotif Pxanrr q Determine P x usin the binomial robabilit formula and table Al 727 l n6 xl p05 2 n9 x7 p8 The Washington Times News E The Washington Times Published in quot El see the text links at the bottom of the page wwwwashtimescom Other Sections vi Fl submit DC 5am October 19 1998 Polls take commanding lead in politics business By August Gribbin THE WASHINGTON TIMES Part one of two E here are folks out there who want to probe your mind They want to know what you think how you feel how you39ll vote and why Even if you don39t tell them they have ways of finding out or at least of surmising They abound in business and industry where their imarketing surveys ultimately determine what you will eat wear read drive and view on television lmportantly their work can be used to slyly in uence your perceptions of the world Many scholars say pollsters now are pivotal in the democratic process Some say they39re wrecking it Yet few people outside the polling industry clearly understand what these hidden persuaders really do or how their work can inform manipulate and at worst deceive It39s generally conceded that polling is indispensable in smart campaigning That39s partly because changes in the size and lifestyles of the electorate prevent candidates from learning about their constituents firsthand Similarly officeholders need poll data to support decisions and for planning ways to implement them But those who find polls destructive say poll results too often dictate the policies of officeholders and candidates who bend with the winds of opinion letting surveys serve for conscience Continued from Front Pag There39s another reason why some see polls as a threat and it also shows how polls can in uence public perception In the 1980 presidential election early exit poll results showed Ronald Reagan a decisive winner The results were released three hours before polling places fileCDocuments20and208ettingsJPLapriseMy20DocumentsStat20 20Was Page 1 of 6 8262003 The Washington Times News fileCDocuments20and2OSettingsJPLapriseMy20DocumentsStat20 20Was Page 2 of 6 closed in the West Many Western voters concluded voting was pointless and didn39t bother to cast ballots The critics notwithstanding political pollsters have emerged as the seers and savants of officeholders office seekers and political pundits They have armed clients with the ability to spot and dodge issues on which they and their constituents may disagree while identifying emotion churning topics that will attract support And in general states Victor Cohn quotSurveys are conducted and often distorted by groups trying to sell rather than report some view Mr Cohn a fellow at the American Statistical Association has authored quotNews amp Numbers a book about reporting statistical information He notes quotAll of us very much including journalists need to temper our acceptance of surveys and polls with some knowledge of their structure and limitations Finding a random sample In fact legitimate survey researchers use the same basic tools questionnaires trained interviewers and the mystifying process called quotscientific sampling That39s a proven method of tapping the opinions of hundreds of millions of people by getting answers from only a small representative and randomly chosen group or quotsamplequot Since nearly everyone these days has a telephone public opinion and political pollsters conduct interviews by phone using quotrandom digit dialing Computers generate a random sample of phone numbers from a list of all working numbers including unlisted ones Kathleen Frankovic poll director for CBS39 television news division says phone interviewing is cheap quick and dependable quotWe can control the phone interviewers and the process better than we could control interviewers we send out on their own making door to door calls she says CBS produces its surveys jointly with the New York Times The two organizations share expenses and expertise maintain phone banks train interviewers organize surveys and the rest Miss Frankovic and Michael Kagay the Times39 news surveys editor report to news executives They attend news meetings and work with the reporters producers and editors assigned to prepare survey stories The polling editor or director develops survey questionnaires working with reporters or TV producers That39s because preparing the right questions in appropriate unbiased language and in the correct order is essential Crafting unbiased questions For example a poll might ask quotWould you vote for someone who favors the slaughter of unborn infants The 8262003 The Washington Times News Page 3 of 6 question is likely to evoke a different response than if the pollster asked quotWould you vote for someone who tolerates abortion Likewise asking several questions about abortion and infanticide before asking quotWould you vote for someone who tolerates abortion is likely to generate a different response than the question alone would get The way Miss Frankovic and Mr Kagay work is basically the way survey researchers and reporters function in the more common situation where outside firms such as the Gallup Organization conduct surveys for the media As all who follow the news know the news media report the results of quottrackingquot polls almost daily during the final phases of national political campaigns They conduct quotexitquot polls on Election Day and frequent even overnight polls after various major political and nonpolitical news events Tracking polls ask identical sample groups the same set of questions each day Results are averaged after two or three days and the most recent polling data replace the oldest That way results can re ect ups and downs over time as opposed to giving a one day snapshot of public preference Because the polling is continuous it39s said to give a quotrolling average of public sentiment as Miss Frankovic phrases it The news media began doing their own polling because public opinion surveys yield frequent fresh and often exclusive stories Significantly though news organizations wanted to free themselves of dependence on what author Cohn calls quotdishonestly worded unreliable surveys paid for by interests activists businesses trade groups and candidates Even if honestly conducted these are usually published only if the results say what the sponsor wants the public to hear Potential to be in uential Like many news reports poll stories help set the public agenda by highlighting issues the public otherwise might not think important or as important as the media see them Polls also allow the public to gauge the gravity and extent of problems But sometimes even good ones can create the illusion of strong public sentiment where none exists David W Moore co managing editor of the Gallup Poll and author of quotThe Superpollsters a history of polling notes surveys mislead at times by asking questions about topics respondents may have little interest in and know nothing about Ask a group of average citizens quotDo you think the United States should encourage construction of a gas pipeline from Siberia to Turkey fileCDocuments20and20SettingsJPLapriseMy20DocumentsStat20 20Was 8262003 The Washington Times News fileCDocuments20and20SettingsJPLapriseMy20DocumentsStat20 20Was Page 4 of 6 Since few people can be expected to understand the issue which they may not have heard about their answers would be of little value Resulting headlines indicating quotUS Citizens Oppose or Favor Russia Gas Linequot would give the misleading impression that the question is a quothot buttonquot issue Polls quotalter people39s perception and have a residual effect on public opinionquot says LaS alle University political scientist Ed Turzanski If they didn39t he argues politicians would not use quotpush pollsquot Push polls ask carefully honed questions that guide or quotpushquot interviewees to a predetermined conclusion For instance they might imply that political candidate Jones is an alcoholic or that a health care bill of rights would send medical costs soaring Such polls actually are pseudo surveys propaganda devices A prime example of a push poll question given by researchers Norman Bradburn and Seymour Sudman in their book quotPolls and Surveysquot is quotAre you in favor of allowing construction union czars the power to shut down an entire construction site because of a dispute with a single contractor thus forcing even more workers to knuckle under to union agenciesquot Polling partisanship Although many political survey research firms work for businesses and lobbyists and turn out newsletters as marketing tools they generally don39t work for the news media Also they limit their work to members of just one political party They are partisans And their work is extensive Says pollster Bruce Blakeman of Wirthlin Worldwide quotIn most campaigns today the pollster is a key strategist He sits at the table and helps decide what kind of advertising to use what areas the candidate should campaign in He is one of the four or six people who make the big tactical and strategic decisionsquot Political pollsters routinely produce tracking and exit polls They also run surveys and conduct quotfocus groupquot sessions At these a trained quotfacilitatorquot engages a small group of randomly selected persons in conversation about a topic as the group39s reactions are secretly monitored Pollsters determine how familiar a candidate39s name is the extent of voters39 devotion to the party and the kind of image the candidate and his opponent projects They quottestquot the candidate39s proposed quotmessagesquot or advertising ideas And they determine which voters the candidate must win over on Election Day what messages will persuade those voters and when and where the messages should be given Pollsters test speeches too They provide members of a 8262003 The Washington Times News selected audience with hand held dials and show them a video of the candidate speaking Viewers turn the dial to indicate the ideas they like and those they dislike The result is a computer generated second by second graph overlaid on videotape that shows the speech39s word by word effect on the audience It reveals quotpower phrases that stir the audience and can be used over and over in subsequent speeches One example President George Bush39s quotpoints of light a phrase that captivated test audiences and ultimately stimulated development of citizen volunteer programs across the nation Revealing voters39 emotions Using specially trained interviewers asking meticulously devised questions during one on one sessions the Wirthlin organization gets at the quotvalues and inner emotions that drive voters39 decision making pollster Blakeman says He won39t explain the precise techniques interviewers employ but he claims they can uncover quotthe issues voters are using to discriminate between candidates and learn why they are important The pollsters then chart how people in different areas feel and build a quotcommunications strategy for quotwhat to say and what to avoid saying in the campaign Depending on the candidate39s inclinations the proprietary information pollsters provide can be used to deal with the electorate39s concerns or to avoid them An oft cited textbook example of issue avoidance came in the Bush Dukakis campaign 10 years ago Polls revealed the public was interested in education health care and the environment Instead of focusing on those issues Mr Bush challenged then Gov Dukakis39 liberalism his policy of furloughing prisoners and his opinion on requiring students to the salute the ag The governor responded in kind The result a campaign about quot ags and furloughs that one columnist called an quotissueless charisma barren campaign ideal for the special art of public opinion manipulation Not all pollsters use all techniques of course Their clients may be unable to afford them Polling costs can range from 7500 for a 15 minute survey of a small congressional district to 30000 and up up up for a 40 or 50 question poll of 800 persons Costs depend on the kind of questions asked the number of subgroups included and a host of other variables Beyond that not all pollsters do polling well Some choose the sample group poorly write inept or biased questions use shoddily trained or untrained interviewers conduct polls when people are unlikely to fileCDocuments20and208ettingsJPLapriseMy20DocumentsStat20 20Was Page 5 of 6 8262003