Cognitive impairment of schizophrenics. A study of the differences in cognitive function between normal individuals and patients diagnosed with schizophrenia was published in the American Journal of Psychiatry (Apr. 2010).

The total time (in minutes) a subject spent on the Trail LO5 Making Test (a standard psychological test) was used as a measure of cognitive function. The researchers theorize that the mean time on the Trail Making Test for schizophrenics will be larger than the corresponding mean for normal subjects. The data for independent random samples of 41 schizophrenics and 49 normal individuals yielded the following results:
Schizophrenia Normal Sample size 41 49 Mean time 104.23 62.24 Standard deviation 45.45 16.34 Based on Perez-Iglesias, R., et al. “White matter integrity and cognitive impairment in first-episode psychosis.” American Journal of Psychiatry, Vol. 167, No. 4, Apr. 2010 (Table 1).

a. Define the parameter of interest to the researchers.

b. Set up the null and alternative hypothesis for testing the researchers’ theory.

c. The researchers conducted the test, part

b, and reported a p-value of .001. What conclusions can you draw from this result? (Use a = .01.)

d. Find a 99% confidence interval for the target parameter.
Interpret the result. Does your conclusion agree with that of part c?