R6G treats cancer by reducing growth rate of a tumor. A group of n1 = 7 rats was given 100 mg of the tumor, and after 48 hours they were given R6G. The animals fasted for 24 hours prior to the drug and 8 hours after. After a week, the tumors were weighed giving a sample average and a sample standard deviation ?????x?¯??????1 = 3.6g and s1 = 0.3g. A control group of n2 = 7 rats which received the same tumor had the sample average and sample standard deviation ?????x?¯??????2 = 7.1g and s2 = 0.7g. Assume that the two populations are normally distributed with unequal variances. Can we conclude that R6G reduces the tumor growth rate on average?
a) Justify your answer using a test of hypothesis at a level of significance of 5%
b) Make a 95% confidence interval for the difference between the mean tumor growths