7-10-1

Confidence Intervals

7-10 Confidence Intervals

A confidence interval is a range of values that has a specified probability of containing the parameter being estimated.

A confidence interval that is too broad makes it difficult to get an idea of where the parameter (actual value) is located. A narrow confidence interval, on the other hand, limits the parameter range and makes it possible to obtain highly accurate results.

The commonly used confidence levels are 68%, 95% and 99%. Raising the confidence level broadens the confidence interval. Conversely, lowering the confidence level narrows the confidence interval, but it also creates the risk that parameters will be missed. With a confidence interval of 95%, for example, there is a 5% probability that a parameter will not be within the interval.

The following is a list of confidence intervals and a description of what each obtains.

Confidence Interval Name

Description

 

 

 

Z Confidence Interval

 

 

1-Sample Z Interval

Calculates the confidence interval for the population mean based on

 

a sample mean and known population standard deviation.

 

 

 

 

 

 

2-Sample Z Interval

Calculates the confidence interval for the difference between

 

population means based on the difference between sample means

 

 

when the population standard deviations are known.

 

1-Prop Z Interval

Calculates the confidence interval for the population proportion

 

based on a single sample proportion.

 

 

 

 

2-Prop Z Interval

Calculates the confidence interval for the difference between

 

population proportions based on the difference between two sample

 

 

proportions.

 

 

 

t Confidence Interval

 

 

1-Sample t Interval

Calculates the confidence interval for the population mean based on

 

a sample mean and a sample standard deviation when the

 

 

population standard deviation is not known.

 

 

 

 

 

Calculates the confidence interval for the difference between

 

2-Sample t Interval

population means based on the difference between sample means

 

and sample standard deviations when the population standard

 

 

 

 

deviations are not known.

 

 

 

kGeneral Confidence Interval Precautions

If you input a C-Level (confidence level) value in the range of 0 <C-Level < 1, the value you input is used. To specify a C-Level of 95%, for example, input “0.95”.

20060301