Estimating a Population Proportion (ch. 9)

Margin of Error depends on 3 factors:

*Level of confidence*: As the level of confidence increases, the margin of error also increases. *Sample size*: As the size of the random sample increases, the margin of error decreases. *Standard deviation of the population*: The more spread there is in the population, the wider our interval will be for a given level of confidence.

Objectives

1) Obtain a point estimate for the population proportion 2) Construct and interpret a confidence interval for the population proportion 3) Determine the sample size necessary for estimating the population proportion within a specified margin of error

Confidence Interval for p^ (Population Proportion)

A confidence interval for an unknown parameter consists of an interval of numbers based on a point estimate. The level of confidence represents the expected proportion of intervals that will contain the parameter if a large number of different samples is obtained. The level of confidence is denoted (1 - α)·100%.

the margin of error decreases

As the sample size increases, ___________________________________

Point Estimate for *p^ (Population Proportion)*

the value of a statistic that estimates the value of a parameter

As the percent confidence increases, the size of the interval increases.

How does increasing the level of confidence affect the size of the margin of​ error, E? -As the percent confidence increases​, the size of the interval decreases. -As the percent confidence increases​, the size of the interval stays the same. -As the percent confidence increases, the size of the interval increases.

As the sample size increases​, the margin of error decreases.

How does increasing the sample size affect the margin of​ error, E? -As the sample size increases​, the margin of error stays the same. -As the sample size increases, the margin of error increases. -As the sample size increases​, the margin of error decreases.

The sample data must come from a population that is normally distributed with no outliers

If the sample size is 16​, what conditions must be satisfied to compute the confidence​ interval? -The sample size must be large and the sample should not have any outliers -The sample data must come from a population that is normally distributed with no outliers -The sample must come from a population that is normally distributed and the sample size must be large.

the sample data must be normally distributed

If the sample size is less than 30, what needs to be true regarding the distribution of the sample data?

Margin of Error

The ________ __ __________ of a confidence interval estimate of a parameter is a measure of how accurate the point estimate is.

the interval size increases

What happens to the size of the interval when the percent of confidence increases?

Confidence Interval

___________ ____________ estimates for the population proportion are of the form *Point estimate ± margin of error*