ESTIMATING the MEAN OF A POPULATION
Confidence Interval Estimates For Large Samples
Assume the following.
 the sample has been randomly selected
 the population standard deviation is known or the sample size is at least 25.
Example
Estimate, with 95% confidence, the lifetime of nine volt batteries using a randomly selected
sample where:
X = 49 hours
s = 4 hours
n = 36
Solution
Lower Limit:
49 - (1.96)(4/6)
49 - (1.3) = 47.7 hrs.
Upper Limit:
49 + (1.96)(4/6)
49 + (1.3) = 50.3 hrs
Interpret
With 95% confidence we say that the mean lifetime of the population of batteries is between 47.7
and 50.3 hours. [With repeated sampling, 95% of the confidence intervals, formed in this
manner, will contain .]
You can use Excel to find the margin of error for this problem:
(1.96)(4/6) = 1.306641
1. From the menu bar, use the function box and go to 'Statistical"
2. On the right side of the screen, choose: 'Confidence'
3. Put the following values in the screen that appears.
For alpha, use:
For Standard_dev, use:
For Size, use:
.05
4
36
(for a 95% confidence interval estimate)
(the standard deviation that is given in the statement of the problem)
(the size of the sample)
4. Click 'okay' and the following formula is generated.
=CONFIDENCE(0.05,4,36)
The cell will show:
1.306641
5. Add 1.306 to the value to get the upper limit.
Subtract 1.306 to the value to get the lower limit.
Confidence Bounds
 Provides a upper or lower bound for the population mean.
 To find a 90% confidence bound, use the z value for a 80% CI estimate.
Goodson/ 3360ci
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