To Projects

IT 403 -- Project 5

Important:   Include all relevant SPSS output; delete all irrelevant SPSS output. The starred questions require a typed answer as well as SPSS output that supports your answer.

One-sample t-tests

• To test the hypothesis that eating fish makes one smarter, a random sample of 12 persons take a fish oil supplement for one year and then are given an IQ test. Here are the results:
  

  116  111  101  120   99   94
  106  115  107  101  110   92
  

  Perform these five parts of a t-test by hand to test the null hypothesis that μ = 100 (the fish oil supplement did not make a significant difference):
  
  1. *State the null and alternative hypothesis.
  2. *Compute the test statistic t = (x - μ) / SE_ave.
  3. *Find a 95% confidence interval I for the test statistic, assuming the null hypothesis.
  4. *If t ∈ I, accept H₀; if t ∉ I, reject H₀.
  5. *Use SPSS to compute the p-value.:
           Analyze >> Compare Means >> One Sample T Test.

Two-sample t-tests

1. Import Sheet1 and Sheet2 of the paper-thicknesses.xls Excel file.
2. Print the two datasets.
3. Perform the following, using the appropriate dataset for each item:
   
   1. *Use Sheet2. Create two boxplots on the same plot for the thicknesses in Batch A and Batch B separately. Are there any outliers?
            Use Graphs >> Chart Builder.  Drag a Simple Boxplot onto the Chart Preview Area. Use Batch as the x-variable and Thickness as the y-variable.
   2. *Use Sheet1. Create normal plots for the thicknesses in Batch A and Batch B separately. Interpret the normal plots.
   3. *Using Sheet1, use SPSS to perform a paired-sample t-test on the Paper Thicknesses data. State the null and alternative hypotheses. What is the t-statistic?  Find a 95% confidence interval for the test statistic. Do you accept or reject the null hypothesis using a 95%-confidence test? What is the p-value?
            Use Analyze >> Compare Means >> Paired Samples t-test.
      Enter BatchA as Variable1 and BatchB as Variable2 for the Paired Variables. The p-value is marked as Sig. (2-tailed).
   4. *Use Sheet2. Use SPSS to perform an independent-sample t-test on the Paper Thicknesses data:
           Use Analyze >> Compare Means >> Independent-Samples T Test
      Two State the null and alternative hypotheses. What is the t-statistic?  Find a 95% confidence interval for the test statistic. Do you accept or reject the null hypothesis. What is the p-value.
4. Using Sheet1, compute the new variable Diff, computed as Batch1 - Batch2.
         Use Transform >> Compute Variable.
5. *Find xbar and SD+ for Diff. What are the sample mean and SD+?
6. *Compute the t-value by hand for the null hypotheses Diff=0, using xbar and SD+ from Question 5.
   
   1. *Is it the same t-value obtained using teh paired-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.
   2. *Is the p-value for H₀: Diff=0 the same as the p-value obtained in Question 3c?
   3. *Do you think the paired-sample t-test or the independent-sample t-test is more appropriate for analyzing the paper thicknesses data?