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 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 41schizophrenics and 49 normal individuals yielded the following results: schizophrenia - sample size: 41, mean time: 104.23, standard deviation: 45.45; normal - sample size: 49, mean time: 62.24, standard deviation: 16.34. Do the data provide significant evidence, at the4.6% level, that the population mean time for patients diagnosed with schizophrenia

exceeds the population mean time for normal individuals by more than 20 points?