Statistics Chapter 9

Front 1

Central Limit Theorom (CLT)

Back 1

States that the sampling distribution model of the sample proportions (and means) is approximately Normal for large n, regardless of the distribution of the population, as long as the observations are independent

Front 2

Confidence interval

Back 2

An interval of values usually of the form:

estimate (plus or minus) margin of error

found from data in such a way that a percentage of all random samples can be expected to yield intervals that capture the true parameter value.

Front 3

Critical value

Back 3

The number of standard errors to move away from the mean of sampling distribution to correspond to the specified level of confidence. The critical value, denoted by an asterisk (z* for a Normal critical value), is usually found from a table or with technology

Front 4

Margin of Error (ME)

Back 4

In a confidence interval, the extent of the interval on either side of the observed statistic value. A margin of error is typically the product of a critical value from the sampling distribution and a standard error from the data. A small margin of error corresponds to a confidence interval that pins down the parameter precisely. A large margin of error corresponds to a confidence interval that gives relatively little information about the estimated parameter.

Front 5

One-proportion z-interval

Back 5

A confidence interval for the true value of a proportion. The confidence interval is

P(hat) plus or minus z*SE(p hat)

where z* is a critical value from the Standard Normal model corresponding to the specific confidence interval

Front 6

Sampling distribution

Back 6

The distribution of a statistic over many independent samples of the same size from the same population

Front 7

Sampling distribution model for a proportion

Back 7

If the independence assumption and randomization condition are met and we expect at least 10 successes and 10 failures, then the sampling distribution of a proportion is well modeled by a Normal Model with a mean equal to the true proportion p, and a standard deviation equal to the square root of ((p x q)/n)

Front 8

Sampling Error

Back 8

The variability we expect to see from sample to sample is often called the sampling error, although sampling variability is a better term

Front 9

Standard error

Back 9

When the standard deviation of the sampling distribution of a statistic is estimated from the data, the resulting statistic is called a Standard Error (SE)

Mean=0 and SD=1.