It is thought that sleep is the key to good learning. Suppose two samples are taken. A sample of 36 Dean's list students reveal they get an average...

It is thought that sleep is the key to good learning. Suppose two samples are taken. A sample of 36 Dean's list students reveal they get an average of 7 hours of sleep a night with sample variance .5. A sample of 49 non Dean's list students reveals they get an average of 6.5 hours of sleep a night with sample variance .7. Suppose we have reason to believe non Dean's list students actually get a difference of half an hour sleep. Using this alternative hypothesis, what is β?