Chapter 12.1, Problem 29E

To determine

To explain why it is not safe to use paired t procedures to do inference about the difference in the mean time to complete the two task.

Explanation of Solution

In the question Mr. Starnes designed a study to examine the questions that does the color in which words are printed affect your ability to read them and so the words themselves affect your ability to name the color in which they are printed. Thus, now from the difference calculated in the previous exercise we will construct the boxplot as follows:

  

Thus, there are three conditions to use the paired t procedures, that is: Random, Normal and Independent.

Therefore, the normal requirement has not been satisfied because the data contains an outlier and the distribution is skewed which is also notable from the histogram constructed in previous exercise $28$ and the sample size is also less than $30$ .