Chapter 5

Section 2 Part 2

Population - entire group of people or items for which

we are collecting data Sample – selections of the population that is used to

make inferences about the population Parameter – a number or percentage that represents

the population Statistic – a number of percentage that represents the

sample Bias – A systematic error in measuring the estimate

favors certain outcomes Sampling Variability – variability between different

samples

Vocabulary Review

We know that surveys can have variability,

how do we take the variability and translate it into a statement of confidence?

The Margin of Error conveys how much confidence we have in the results of a survey by translating the sampling variability.

What do samples tell us?

Given the following statement:

If we took many samples using the same method we used to get this one sample, 95% of the samples would give a result within plus or minus 3 percentage points of the truth about the population.

The margin of error is the plus or minus 3 percentage points

95% of all samples came close to the truth, but 5% miss the mark by more than the margin of error. We don’t know the truth about the population, so we don’t know if our sample is one of the 95% that hit or one of the 5% that miss. We say we are 95% confident that truth lies within the margin of error.

What a margin of error means?

If you use the sample proportion p from a

simple random sample of size n to estimate an unknown population proportion, p, then the margin of error for 95% confidence is roughly equal to 1 /

Actual Formula for 95% confidence interval 1.96 ( )

Method for Margin of Error

In a survey of 705 people, 14% said that they watch

television more than 12 hours per week. What is the margin of error?

The quick method reveals an important fact about how margins of error behave. Since the sample size n appears in the denominator of the fraction, larger samples have smaller margins of error.

Example

Given the margin of error….how many people

were sampled

± 5.5%

Working backwards

A Confidence Statement has two parts: a

margin of error and a level of confidence. The margin of error says how close the sample statistics lies to the population parameter. The level of confidence says that percent of all possible samples satisfy the margin of error.

Confidence Statements

Formula for Confidence interval:

statistic of SD valuecritical statisticCI

p̂

npp 1*z

Normal curve

Note: For confidence intervals, we DO NOT know p – so we MUST substitute p-hat for p in both the SD & when checking assumptions.

A May 2000 Gallup Poll found that 38% of a random sample of 1012 adults said that they believe in ghosts. Find a 95% confidence interval for the true proportion of adults who believe in ghost.

41,.35.1012

)62(.38.96.138.

1*ˆ

npp

zP

We are 95% confident that the true proportion of adults who believe in ghosts is between 35% and 41%.

Standard Conclusion

We are 95% confident that the true proportion of ___________________ is between ______% and ______%.

The conclusion of a confidence statement always

applies to the population, not the sample Our conclusion about the population is never

completely certain A sample survey can choose to use a confidence

level other than 95%. A higher confidence level means and larger margin of error

It is usual to report the margin of error for 95% confidence

Want a smaller margin of error with the same confidence? Take a larger sample

Important hints for interpreting confidence

statements

The variability of a statistics from a random

sample does not depend on the size of the population, as long as the population is at least 10 times larger than the sample

10 * n < Population

Population size doesn’t matter

Example

Homework