Chapter 12.1, Problem 28E

To determine

To explain do the data provide evidence of a difference in the average time required to perform the two tasks and include an appropriate graph and numerical summaries.

Answer to Problem 28E

Yes, the data provide evidence of a difference in the average time required to perform the two tasks.

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, the table for the difference of the data is calculated as:

  

The formulas that is used in excel are as:

  $\begin{array}{l}\text{=AVERAGE(number1,number2,}\mathrm{..}\text{)}\\ \text{=MEDIAN(number1,number2,}\mathrm{..}\text{)}\\ =\text{QUARTILE(array,quart)}\\ \text{=MAX(number1,number2,}\mathrm{..}\text{)}\\ =\text{MIN(number1,number2,}\mathrm{..}\text{)}\\ \text{=STDEV(number1,number2,}\mathrm{..}\text{)}\end{array}$

And the histogram can be constructed from the data given in the question and the numerical summaries can also be calculated by using the excel technology as:

  

  

Therefore, the data provide evidence of a difference because all the bars of the histogram above lie to the left of the zero. Moreover, the maximum is zero and the other values are all negative. Thus, the mean is $-6.5626$ which is also negative and the standard deviation is $4.6615$ .