Chapter 3 1

Chapter 3

What Do Samples Tell Us?

Chapter 3 2

Thought Question 1

During a medical exam, the doctor measures your cholesterol two times. Do you think both measurements would be exactly the same? Why or why not?

Chapter 3 3

Thought Question 2

To estimate the percentage of all adults who have an internet connection in their homes, a properly chosen sample of 1100 adults across the U.S. was sampled, and 60% said “yes”. How close do you think that is to the percentage of the entire country who have an internet connection? Within 30%? 10%? 5%? 1%? Exactly the same?

Chapter 3 4

Sampling Terminology Parameter

– fixed, unknown number that describes the population Statistic

– known value calculated from a sample– a statistic is used to estimate a parameter

Bias– in repeated samples, the sample statistic consistently

misses the population parameter in the same direction Variability

– different samples from the same population may yield different values of the sample statistic

Chapter 3 5

Bias and Variability

Consider shooting arrows at a target:Bias means the archer systematically misses in the same direction. Variability means that the arrows are scattered.

Chapter 3 6

Sampling Strategy

To reduce bias, use random sampling

To reduce variability, use larger samples– estimates from random samples will be closer to

the true values in the population if the samples are larger

– how close will they be? margin of error

Chapter 3 7

The proportion of a population that has some outcome (“success”) is p.

The proportion of successes in a sample is measured by the sample proportion:

Proportions

sample the in nsobservatio of number totalsample the in successes of numberp̂

“p-hat”

Chapter 3 8

The amount by which the proportion obtained from the sample ( ) will differ from the true population proportion (p) rarely exceeds the margin of error.

Margin of Error

p̂

Typical margin of error: 1/sqrt(n)– In 95% of surveys, the sample proportion will

not differ from the population proportion by any more than the margin of error. (“95% confidence”)

demo

Chapter 3 9

Case Study

62% say it should be guaranteedby the government

same as in 2000, up 6 points from 1996

31% say it is not the responsibilityof the government

Guaranteed Health Insurance in the U.S.? New York Times/CBS News Poll, January 2006

Chapter 3 10

How the Poll was Conducted

This New York Times/CBS News poll was based on telephone interviews conducted January 20 through January 25, 2006 with 1,229 adults throughout the United States. The survey has a random sampling error of approx. ±3 percent.

Case Study

Chapter 3 11

Conclusion (Confidence statement)

For the proportion of the population who favor guaranteed health insurance, the sample proportion was = .62 (62%) and the margin of error was ±.03 (3%). We can then say that “we are 95% confident that the proportion of the population who favor guaranteed health insurance was between .59 and .65 (59% and 65%).”

Case Study

p̂

Chapter 3 12

Key Concepts

Parameter versus Statistic Bias and Variability Margin of Error Confidence Statements