Confidence Interval
When using the t-Distribution
x
s
n

1
t
( df , / 2 )
s
7041.4
1610.3
7
0.010
TRUE
Inputs
Outputs
the sample mean; it is the center point of the confidence interval
the sample's standard deviation
the sample size
6 degrees of freedom
We desire this level of confidence.
99.00% confidence interval
AllInputsOkay
0.9900 LevelOfConfidence = 1 - alpha
99%
confidence interval
3.707428 ConfidenceCoefficient = tINV(0.01,6)
a) Lookup in table of Critical Values of the t-Distribution
or b) Excel: =TINV(alpha, df) or c) TI-84: invT(
0.0050 α/2 is the area in the right tail above this z value
0.0050 α/2 is the area in the left tail below -z, too
0.0100 The total area in the two tails is α
0.9900 The area in the middle, between the two tails, is 1-α
608.6362 = StandardDeviation of the Sample/SQRT(SampleSize)
n
Result
from
2256.475
E, MaximumErrorOfEstimate
= ConfindenceCoefficient * StandardErrorOfTheMean
The 99% confidence interval for the Mean is:
to
=SampleMean - MaximumErrorOfEstimate to SampleMean + MaximumErrorOfEstimate
4784.925
to
9297.875
Confidence Interval
Inputs
Outputs
When the population standard deviation, σ, is known (or for "large enough" sample size n)
x
s
n

from
563.2
87.9
10
0.050
TRUE
the sample mean; it is the center point of the confidence interval
the sample's standard deviation
the sample size
9 degrees of freedom
We desire this level of confidence.
95.00% confidence interval
AllInputsOkay
to
There is the CONFIDENCE() function for the z case but no corresponding function for the t case.
TI-84
1)
2)
3)
4)
STAT menu
Right arrow to TESTS submenu
8:Zinterval
Choose "Data" or "Stats"
"Data"
"Stats"
Use this if you have stored
data in a TI-84 "List".
Use this if you have the
mean and sample size
without a TI-84 "List".
5) Highlight "Calculate" and press Enter when your inputs are complete
Example: [Blu4 page 364], unlabeled data from their MegaStat illustration
"Stats" screen input:
Results:
Remark: The book's interval is (500.320,626.080)
Somebody is using more precision than somebody else.
Excel's answer:
500.3201281 to
626.0799
But their MegaStat is an Excel add-in, so no wonder they agree.
There have been mentions somewhere of Excel making changes in the interest of accuracy.
Excel TINV(.05,9)=
2.2621571581736
TI-84 invT(.975,9)=
2.262157158
That's not the problem.
The problem is that the MegaStat printout showed std. dev at 87.9 but the calculator used
the more accurate 87.85821912