Bush's lead gets smaller in poll By Susan Page, USA TODAY WASHINGTON — President Bush leads Sen. John Kerry by 8 percentage points among likely voters,

• Bush's lead gets smaller in poll

• By Susan Page,

• USA TODAY WASHINGTON — President Bush leads Sen. John Kerry by 8 percentage points among likely voters, the latest USA TODAY/ CNN/Gallup Poll shows. That is a smaller advantage than the president held in mid-September but shows him maintaining a durable edge in a race that was essentially tied for months.

Results based on likely voters are based on the sub

sample of 758 survey respondents deemed most

likely to vote in the November 2004 General Election. The margin of

sampling error is ±4 percentage points.

4 out of 5 core 120 students want more tests

COLLECTING STATISTICAL DATA

When information is packaged in numerical form, it is called data. (page 447)

Statistics is the science of dealing with data. This includes gathering data, organizing data, interpreting data, and understanding data. (page 447)

COLLECTING STATISTICAL DATA

60 years ago H.G. Wells predicted:“Statistical reasoning will some day be as important to efficient citizenship as the ability to read and write.”

SPORTS HEALTH

WEATHERBUSINESS

The N-value is an accurate head count of every member of a population. (page 448)

Do not confuse the N-value with the population itself.

The group of individuals or objects to which a statistical statement refers is called the population. (page 448)

Determining the N-Value of a population

Census: Collecting data from every member of the population (page 450)

When populations are small and accessible, one can actually get an exact N-value by simply counting “heads”.

The U.S. Census• “Taxation and Representation” - Used to draw

legislation districts, allocate federal funds, to determine plans for business and industry, …

• United States population is defined as consisting of “all persons physically present and permanently residing in the United States.”

• Census used to collect information about, age, race, sex, ethnicity, marital status, income, employment, …

The N-value N=430 is only an estimate.

Collecting data from a selected subgroup of a population and then using those data to draw a conclusion and make statistical inferences about the entire population is called conducting a survey. The subgroup of the population from which the data is collected is called a sample. (page 452)

Sampling

• Try to get the sample to represent the population– Every member should have the opportunity to be

chosen• This is not always possible

– public opinion on presidential voting in upcoming election

– If the sample is representative of the population, we can draw trustworthy conclusions.

• Study 1: You are conducting a poll of 1,500 people to predict the outcome of the next Pennsylvania Democratic Presidential Primary. You randomly sample from a list of registered voters in the state. 45% say they will vote for Hillary Clinton.

• Study 2: In order to estimate how effective Mr. Evans is in his Core 98 class, he gives 5 students in each of his two sections a survey on which they rate his effectiveness on a scale of 1-10. He chooses students from each section in the following way: one that is getting an “A”, one that is getting a “B”, one that is getting a “C”, etc…

• Study 3: You want to decide if residents of Wilkes-Barre prefer Coca-cola or Pepsi. You set up a taste test booth at one of the local supermarkets and offer free samples in return for their opinion.

STEP 1. The Capture: Capture (choose) a sample of size , tag (mark, identify) the animals (objects, people), and release them back into the general population.

1n

2nSTEP 2. The Recapture: After a certain period of time, capture a new sample of size , and take an exact head count of the tagged individuals (i.e., those that were also in the first sample). Let’s call this number k.

THE CAPTURE-RECAPTURE METHOD: ESTIMATING THE N-VALUE OF A POPULATION BY SAMPLING

(page 460)

The ratio is approximately equal to the ratio . From this we get: .

2n/k N/n1

N

n

n

k 1

2

Example. You want to estimate how many fish there are in a small pond. Suppose you capture 500 fish, tag them, and throw them back in the pond. After a couple of days, you go back to the pond and capture 120 fish, of which 30 are tagged. Give an estimate of the N-value of the fish population in the pond.

Homework

• Read pages 446 - 451, 460 - 461 (capture-recapture method)