Chapter 8 Interval Estimation

Interval Estimate of population proportion

Is equal to pbar +/- the z score of the upper tail (1 - confidence coefficient) multiplied by (the square root of (pbar times (1 - pbar)) / the sample size)

Sample Size of an interval estimate of a population proportion

p* is the planning value, or the pbar of a sample proportion. E is the size of the margin of error.

Interval Estimate of a population proportion

pbar +/- the margin of error.

Margin of Error

The +/- value added to and subtracted from a point estimate in order to develop an interval estimate of a population parameter.

T Distribution

A family of probability distributions that can be used to develop an interval estimate of a population mean whenever the population standard deviation sigma is unknown and is estimated by the sample standard deviation s.

Degrees of freedom

A parameter of the t distribution. When the t distribution is used in the computation of an interval estimate of a population mean, the appropriate t distribution has n - 1 degrees of freedom, when n is the size of the simple random sample.

Interval Estimate

An estimate of a population parameter that provides an interval believed to contain the value of the parameter. Usually takes the form point estimate +/- margin of error. Computed by adding and subtracting the margin of error to the point estimate. Purpose is to provide information about how close the point estimate, provided by the sample, is to the value of the population parameter.

Confidence Interval

Another name for an interval estimate.

Interval estimate when sigma is unknown

Is equal to xbar plus or minus the t value of the upper tail (1 - confidence coefficient) multiplied by the (sample standard deviation/ the square root of n). The t distribution has an n - 1 degrees of freedom. (t distribution chart uses degrees of freedom).

Sigma is Known

The case when historical data or other information provides a good value for the population standard deviation prior to taking a sample. The interval estimation procedure uses this known value of sigma in computing the margin of error.

Confidence Level

The confidence associated with an interval estimate. For example, if an interval estimation procedure provides intervals such that 95% of the intervals formed using the procedure will include the population parameter, the interval estimate to be constructed at the 95% confidence level.

Confidence Coefficient

The confidence level expressed as a decimal value. For example, .95 is the confidence coefficient for a 95% confidence level.

Sigma Unknown

The more common case when no good basis exists for estimating the population standard deviation prior to taking the sample. The interval estimation procedure uses the sample standard deviation s in computing the margin of error.

Level of Significance

The probability that the interval estimation procedure will generate an interval that does not contain mu.

Interval Estimate when Sigma is Known

is equal to xbar +/- the z score of the upper tail (1-confidence coefficient) multiplied by (sigma over the square root of the sample size). This will give the interval in which the population mean will be located given the confidence level.