Central Limit Theorem Excel Worksheet by crf13445

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									  • SPSS does not calculate confidence intervals for proportions.
  • The Excel spreadsheet that I used to calculate the proportions
    can be downloaded from Kay’s Excel spreadsheets.




12/15/2010                                                    Slide 1
             The introductory statement in the question indicates:
             • The data set to use: GSS2000R.SAV
             • The task to accomplish: a confidence interval for proportions
             • The variable to use in the analysis: self-employment [wrkslf].
             • The category to use for the confidence interval: self-employed




12/15/2010                                                                      Slide 2
             The first statement asks about the level of
             measurement. To compute a confidence interval
             for proportions, the variable must be categorical.

             We will use a frequency distribution to get a list of
             the values for the variable.




12/15/2010                                                           Slide 3
             To compute the frequency distribution,
             select the Descriptive Statistics > Frequencies
             command from the Analyze menu.`




12/15/2010                                                     Slide 4
             First, we move the
             variable wrkslf to the
             Variable(s) list box.




                                      Second, click on the
                                      OK button to
                                      produce the output.




12/15/2010                                                   Slide 5
             The variable includes
             two categories,
             justifying its use as a
             categorical variable.




12/15/2010                             Slide 6
             Since the variable self-employment [wrkslf]
             can be used as a categorical variable, we
             mark the statement as correct.




12/15/2010                                                 Slide 7
             The second statement asks about the
             sample size requirements. We can use the
             frequency distribution to get the number
             and percentage of cases in each category.




12/15/2010                                               Slide 8
             The sample size is large enough to make the sampling
             model for the sample proportions approximately normal
             based on the Central Limit Theorem if there are 10 or more
             cases in both the target category for the confidence interval
             and the other category in the distribution of the variable.




                                        There were 32 in the category "self-
                                        employed". With 250 valid cases in
                                        the distribution, the number of cases
                                        in the other category was 218.

                                        Both groups used to compute the
                                        confidence interval had the required
                                        minimum of 10 cases. The sample
                                        size requirement is satisfied.



12/15/2010                                                                      Slide 9
             Both groups used to compute the
             confidence interval had the required
             minimum of 10 cases. The sample size
             requirement is satisfied.

             Mark the check box for a correct answer.




12/15/2010                                              Slide 10
             The next question asks us about
             the 95% confidence interval.




                                        SPSS does not compute the
                                        confidence interval for a
                                        proportion. We will use Excel to
                                        calculate the confidence interval.




12/15/2010                                                                   Slide 11
             To compute the confidence interval in Excel, we need two
             items of information from the SPSS frequency table:
             • The valid percent in the target category
             • The total number of valid cases




12/15/2010                                                              Slide 12
             When you open the Excel workbook
             ConfidenceIntervalForProportions.xls,
             you will see the following.
                                                     Directions for using the
                                                     worksheet are shown in
                                                     rows 1 and 2.




                                                        Unless you unprotect the
                                                        worksheet, the only cells
                                                        you can enter data in are
                                                        B4 and B6.




                                                           The worksheet includes the
                                                           formulas for all three of the
                                                           confidence intervals of interest:
                                                           90%, 95%, and 99%.




12/15/2010                                                                                     Slide 13
             This view shows the
             formulas that were
             entered in each of the
             orange cells that
             calculate the results.

             You should not have
             to change them.




12/15/2010                            Slide 14
             When cells B4 and B6 are
             empty, this is what the
             worksheet will look like.




12/15/2010                               Slide 15
             Next, we enter data from
             the frequency table to
             compute the interval.




                                        The proportion of survey
                                        respondents who were
                                        self-employed was 0.128.




                                              The proportion of survey
                                              respondents in the categories
                                              other than self-employed
                                              was 0.872 (1.00 - 0.128).




12/15/2010                                                                    Slide 16
             I entered the number of
             valid cases from the SPSS
             frequency table.




                 To compute the standard error based on
                 the sample proportion, we multiply the
                 proportion in the category (0.1280)
                 times the proportion in other categories
                 (0.8720), divide by the number of valid
                 cases (250), and compute the square
                 root of the result [square root(0.1208 x
                 0.8702 ÷ 250) = 0.0211].




12/15/2010                                          Slide 17
             For a 95% confidence interval, we
             compute the margin of error by
             multiplying the standard error by
             1.96 (1.96 x 0.0211 = 0.0414).




12/15/2010                                       Slide 18
             The lower bound of the 95%
             confidence interval is computed by
             subtracting the margin of error from
             the proportion in the target category
             (0.1280 - 0.0414 = 0.0866). The upper
             bound of the 95% confidence interval
             is computed by adding the margin of
             error to the proportion in the target
             category (0.1280 + 0.0414 = 0.1694).




12/15/2010                                       Slide 19
                    The lower bound of the 95% confidence
                    interval is 0.0866 (or 8.7%). The upper
                    bound of the 95% confidence interval is
                    0.1694 (or 16.9%).




             The statement that "we can be 95%
             confident that between 8.7% and 16.9%
             of all survey respondents were self-
             employed" is correct.

             Mark the check box for a correct answer.




12/15/2010                                                    Slide 20
             If we violate the level of measurement or
             sample size requirement, it not appropriate
             to compute the confidence interval. In this
             case, we would mark “None of the above.”




12/15/2010                                                 Slide 21
                                Variable can be               Do not mark
                                                      No       check box.
                            treated as categorical?

Problem will state target                                  Mark only “None of
category. All other                                           the above.”
categories are combined               Yes
into “other” category.                                           Stop.
                               Mark statement
                                 check box.




                             10+ subjects in target            Do not mark
                                                      No        check box.
                             and other categories?

                                                            Mark only “None of
                                                               the above.”
                                       Yes
                                                                  Stop.
                                Mark statement
                                  check box.




12/15/2010                                                                       Slide 22
             Confidence interval        Do not mark
                                   No    check box.
              stated correctly?

                                           Stop.
                    Yes

                                                      We do not mark “None
              Mark statement                          of the above” because
                check box.                            level of measurement
                                                      and sample size should
                                                      be marked if we got to
                                                      this step.




12/15/2010                                                            Slide 23

								
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