Using hypothesis tests for variance and two means:
1. Two independent samples were taken. For the first 42 elements, the mean was 32.3 and the variance 9. The second sample of 67 elements had a mean of 34 and a variance of 12. With alpha = 0.05, test if there is enough evidence to show that the second population has a higher mean
2. Two research laboratories have independently produced medication that relieves the discomfort of arthritis. The first medication was tested in a group of 90 people suffering from the disease and produced an average of 8.5 hours of relief, with a standard deviation of 1.8 hours. The second medication was tested on 80 people and produced an average of 7.9 hours of relief with a standard deviation of 2.1 hours. At a significance level of .05 does the second medication provide a significantly shorter period of relief?