An experiment was carried out to determine the effect of sleep deprivation on reaction time. The 4 levels of sleep deprivation used were 12, 18, 24, and 30 hours. The researchers measured the reaction time to the onset of a light (in hundreths of a second). Use the .05 level of significance in your tests.

The data can be found at http://www.uvm.edu/~rsingle/stat231/data/other/sleep-deprivation.dat . You can read in the data using the FILENAME command with the URL subcommand in SAS, or save a local copy of the file and read it in from there.

a. Test the hypothesis that the amount of sleep deprivation, assuming at least 12 hours of deprivation, does not affect reaction time.

b. Test the hypothesis that there is no difference between the reaction time after 30 hours compared with the average reaction time for the other deprivation amounts.

c. Test the hypothesis that there is no difference between the reaction time after at least one day compared with the reaction time after less than one day.

d. Are the contrasts used in parts (b) and (c) orthogonal? Show why or why not.

e. Construct a contrast that is both orthogonal to the contrast in (b) and in (c).

f. Determine if there is a significant linear trend in the data, using an appropriate contrast at the .05 level of significance. Test for the significance of each of the orthogonal nonlinear contrasts.

g. Write the simplest polynomial equation (in terms of orthogonal polynomial coefficients as in equation 3.15 in the text) necessary to adequately describe the trend based on your results in (f) and predict the reaction time for each level of sleep deprivation based on this model.

h. Compute the proportion of variance in reaction times that is accounted for by the linear contrast. Do the same for any other significant contrast from (f). What do you conclude about the importance of the different contrasts?