Overview of Confidence Intervals (2 of 2)
Next section: Mean, σ known
An excellent way to specify the precision is to construct a
confidence interval. If the number of digits remembered for the 10 students
were: 4, 4, 5, 5, 5, 6, 6, 7, 8, 9 then the estimated value of μ
would be 5.9 and the 95% confidence interval would range from 4.71 to 7.09.
(
Click here to see how to compute the interval.)
The wider the interval, the more confident you are that it contains the
parameter. The 99% confidence interval is therefore wider than the 95%
confidence interval and extends from 4.19 to 7.61.
Below are shown some examples of possible confidence intervals.
Although the parameter μ
1 - μ
2
represents the difference between two means, it is still valid to think
of it as one parameter; π
1 - π
2
can also be thought of as one parameter.
Lower Limit |
|
Parameter |
|
Upper Limit |
0.2 |
≤ |
π |
≤ |
0.7 |
-3.2 |
≤ |
μ |
≤ |
4.5 |
3.5 |
≤ |
μ1 - μ2 |
≤ |
7.9 |
0.4 |
≤ |
π |
≤ |
0.8 |
0.3 |
≤ |
π1 - π2 |
≤ |
0.7 |
Next section: Mean, σ known