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IT 223 -- Project 5

Two-sample t-tests

• Important:   Include all relevane SPSS output; delete all irrelevant SPSS output. Type your answers to the starred questions at the beginning of the MS Word file the also contains the SPSS output. Questions with a star (*) MUST have a typed response. Questions is two stars (**) must have one response for the complete dataset and another response for the dataset with the outlier or outliers deleted.
  1. *Explain how the data were collected. Were there any problems with the data collection.

  2. Open the paper-airplanes.xls dataset.

  3. Compute the new variables Large and Small which are the flight lengths in inches of the large and small airplanes, respectively. Use Transform >> Compute Variables.

  4. Give labels to the variables Large and Small in the two datasets. Check to see that they are both Scale variables.

  5. Print the two datasets.

  6. Perform the following, using the appropriate dataset for each item:
     1. **Create two boxplots for the Large and Small airplane distances separately. Are there any outliers?

     2. **Create normal plots for the Large and Small airplane distances. Interpret the normal plots.

     3. **Use SPSS to perform a paired-sample t-test on the Paper Airplane data. State the null and alternative hypotheses. What is the t-statistic? What is the p-value? Do you accept or reject the null hypothesis using a 95%-confidence test?
        Use Analyze >> Compare Means >> Paired Samples t-test. Enter Large as Variable1 and Small as Variable2 for the Paired Variables.

        The p-value is marked as Sig. (2-tailed).

  7. Remove any rows that contain outliers. Then repeat steps 6a through 6c with the outlier(s) removed.

     Answer Questions 8 through 10 only for the dataset with the outlier(s) removed.

  8. Compute the new variable Diff, which is computed as Large - Small.
     Use Transform >> Compute Variable.

  9. *Compute xbar and SD+ for Diff. What are the sample mean and SD+?

  10. *Compute the t-value by hand for the null hypotheses Diff=0, using xbar and SD+ from Question 9
      1. *Is this t-value the same as the t-value obtained in Question 6c without the outlier(s)?

      2. *Is it the same t-value obtained using a one-sample t-test. (Include the SPSS output from the one-sample t-test for the null hypothesis Diff=0.)
         Use Analyze >> Compare Means >> One-sample t-test. Use Diff as the test variable and 0 as the test value.

      3. *Is the p-value for H₀: Diff=0 the same as the p-value obtained in Question 6c without the outlier(s)?

  11. *How could the experiment be improved to obtain more better results?