Typing again Nick (see Exercise 19) designed a follow-up experiment to see if having Music or Television on would affect his typing speed. In particular, he’d like to know if he can type just as effectively with the music and/or the TV on while he types. He ran each combination of Music and Television on or off 8 times, recording the net number of words typed (words typed minus mistakes).

Partial boxplots and interaction plots show:

The ANOVA table shows:

a) What are the null and alternative hypotheses for the main effects?

b) Given the partial boxplots, what do you suspect the F-test will say about the two main effects?

c) Should he consider fitting an interaction term to the model? Why or why not?

d) If he does fit an interaction term, do you suspect it will be significant on the basis of the interaction plot?
Explain.

e) What effects appear to be significant?

f) Describe the effects of the factors.
g) What is the size of the estimated standard deviation of the errors? Does this seem reasonable given the partial boxplots? Explain.
h) If Nick wants to increase his typing speed, what recommendations would you give him?
i) What reservations, if any, do you have about the conclusions?

Television Effect (WPM) 47.5 45.0 42.5 40.0 43 Mean Speed (WPM) Off Television HO On 47.5 Music Effect (WPM) 400 40.0 42.5 45.0 40 Off On Television HO Off Music 5. 80 On