EXAMPLE: A random sample of 676 American men between the ages of 45 and 65 yielded a mean energy intake per day of 2189 calories, and a standard deviation of 949 calories. Construct a 99% confidence interval for .

In this example we are given a standard deviation based on a sample (population standard deviation is unknown, and n 30). Therefore we will use the formula:

n

szx 2/

__

From the given information we have:

676n 2189__

x 949s

575.22/ zand confidence level = 99% or .99 which corresponds to:

The 99% confidence interval for is given by:

01.209599.932189676

949575.221892/

__

n

szx

and

99.228299.932189676

949575.221892/

__

n

szx

In Words: We are 99% confident that the mean energy intake of all American men between the ages of 45 and 65 is between 2095.01 and 2282.99 calories

or

In Notation:The 99% confidence interval for may be presented in any of three ways:

ANATOMY OF A CONFIDENCE INTERVAL FOR WHERE n 30

When SIGMA, , is UNKNOWN and n 30When SIGMA, , is KNOWN and n 30

or

)99.228201.2095( 99.930.2189 )99.2282,01.2095( [calories]

EXAMPLE: The National Center for Educational Statistics surveyed 4400 college graduates about the lengths of time required to earn their bachelor’s degree. The mean was found to be 5.15 years. Prior studies have found a standard deviation of 1.68 years. Construct a 98% confidence interval for .

In this example we are given a known standard deviation and the sample size is 30. Therefore we will use the formula:

nx z

2

From the given information we have:

4400n 15.5__

x

and confidence level = 98% or .98 which corresponds to: 33.22/ z

The 98% confidence interval for is given by:

059.15.54400

68.133.215.5

2

n

x z

(here: 5.15 - .059 = 5.091 yrs and 5.51 + .059 = 5.209 yrs.)

In Words: We are 98% confident that the mean years to obtain a bachelor’s degree is between 5.091 years and 5.209 years.

In Notation:The 98% confidence interval for may be presented in any of three ways:

)209.5091.5( or

or

059.15.5

[years])209.5,091.5(