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IT 223 -- Project 5

Important:   Include all relevant R output, and the R statements that produces this output. The starred questions require a typed answer as well as R 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 R to compute the p-value.

Two-sample t-tests

1. Import Sheet1 and Sheet2 of the CSV file paper-thicknesses.txt
2. Print the two datasets.
3. Perform the following, using the appropriate dataset for each item:
   
   1. *Use R to create two boxplots on the same plot for the thicknesses in Batch A and Batch B separately. Are there any outliers?
   2. *Use R to create normal plots for the thicknesses in Batch A and Batch B separately. Interpret the normal plots.
   3. *Use R 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?
      
4. *Find xbar and SD+ for Diff, where Diff is the column of differences for BatchA and BatchB. What are the sample mean and SD+ for the values in the Diff column?
5. *Compute the t-value by hand for the null hypotheses Diff=0, using xbar and SD+ from Question 5.
   
   1. *Is the p-value for H₀: Diff=0 the same as the p-value obtained in Question 3c?