# intervals

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```					Introduction:
This file contains three worksheets. The sheet "Confidence Intervals" has the templates to
determine the confidence intervals and sample sizes. The remaining two sheets are Figures 10A.5
and 10A.6 from pages 441 and 442 of the Text. You can use these to study how to calculate probabilities
or determine critical values using the t-distribution.

Instructions:
The templates are self explanatory. You provide the data in the input area section and that is about it.
Refer to the demonstration problems in Appendix 10A for further detail.

Note on data "bleed through" on the templates:
Our objective has been to try to show you how to use Excel to do certain tasks. The template in
this file is an example of how you can set Excel up to do a certain statistical procedure. An issue
which comes up is depending on how the template and the formulas are written, one portion of
the spreadsheet can have data from a previous problem whereas another part will have the answers
you want. There are many ways to handle this. One way is to clear the input area after each use.
If you simply leave the input cells blank, then some or all of the output cells with show error messages
like REF! If that does not bother you then fine. Another way is to set up your formulas so that when you
clear the input cells by entering "na", the output cells echo this input. See the template for interval
estimation of the mean. We did not do this for the rest of the template. We left it for you to mimic us if you
wanted to. Or to modify as you saw fit.

This bleedthrough is an issue that will not go away in subdequent chapters. Please be aware of it.
We will not make explicit references to this anymore.
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Raw data                      User Input                                            Confidence Intervals

Inputs for estimating the population mean                      Interval estimation of the population mean
Confidence level                                  na           Critical z_or_t
Sample mean                                       na           Sample mean
Sample standard deviation                                      Standard error of the mean
Number of observations                            na                       w/FPC
Population size (enter 0 if unknown)                           Lower limit
Sigma (enter 0 if unknown)                                     Upper limit
Sampling Distribution (enter ="z" or ="t" )

Sample size estimation for the mean
Maximum allowable error                           na           Required sample size

Inputs for estimating the population proportion                Interval estimation of the population prop
Confidence level                                       0.95    Critical z
Number of successes                                       90   Sample proportion
Number of trials (I.e. sample size)                     300    Standard error
Sample proportion                                        0.3               w/FPC
Population size (enter 0 if unknown)                       0   Lower limit
Upper limit

Sample size estimation for the proportion
Maximum allowable error                                0.05    Required sample size
Estimated sample proportion                             0.3
Confidence Intervals

stimation of the population mean
na
na
error of the mean      na
na
na
na

na

stimation of the population proportion
1.959963985
0.3
0.026457513
0.026457513
0.248144227
0.351855773

322.6825409
Probability calculations using the t-distribution

Mu              56000       62000       62000       62000        62000
x-bar           64000       64000       66000       56000        60000
s               17250       19750       19750       19750        19750
n                  26          19          19          19           19

t-value     2.364763 0.441407 0.882815           -1.32422      -0.44141

Required Probabilities:

a.         P(x-bar > 64000) = P(t > 2.365) = TDIST(2.365, 25, 1)
b.1        P(x-bar > 64000) = P(t > 0.4414) = TDIST(0.4414,18,1)
b.2.       P(x-bar < 66000) = P(t< 0.8828) = 1 - TDIST(0.8828, 18, 1)
b.3        P(x-bar > 56000) = P(t > -1.32422) = 1-TDIST(1.324,18,1)
b.4        P(x-bar < 60000) = P(t < -0.44141) = TDIST(0.44141, 18, 1)
b.5        P(56000 < x-bar < 66000) = P(-1.32422 < t < 0.8828) = 1-TDIST(0.88,18,1) - TDIST(1.32422, 18, 1)
0.01305
0.33209
0.805509
0.898964
0.332086
DIST(1.32422, 18, 1)   0.703771
Finding critical t-values using TINV

Area         Direction               Formula                     Critical t
0.1   right-tail              TINV(0.20, 12)               1.356217
0.05   right-tail              TINV(0.10, 12)               1.782288
0.025    left-tail             - TINV(0.05, 12)               -2.17881
0.9725    left-tail               TINV(2*(1-0.9725), 14)       2.093403

```
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 views: 2 posted: 8/4/2012 language: English pages: 7