6. A company claims that it has developed a genetically modified watermelon that yields on average heavier watermelon than other varieties. An experimenter wishes to test the claim on a small scale before he/she commits to a full-scale planting. Seven genetically modified watermelons are grown from seeds along with seven other watermelons. In the end of the season, the weight of the resulting watermelons in pound are recorded as follows. Genetically Modified: 10, 13.5, 12.5, 13.5, 12, 11, 13 Regular: 10.5, 11, 10, 9, 11.5, 10,10.5 (a) (8 marks) Let #, be the mean weight of the genetically modified watermelons. Test the null hypothesis #, = 12 against the alternative hypothesis #, > 12 at the 0.05 level of significance. What assumptions are needed for the validity of the test? (b) (8 marks) Do the genetically modified watermelons tend to be heavier on average than those regular watermelons? Carry out a test at a = 0.05 level of significance using both the p-value approach and the critical region approach (if you cannot get the exact value of p-value, you can give a range of p-value). Clearly write down the hypotheses, test statistic, critical region and p-value for the test. What assumptions are needed for the validity of the test? (c) (8 marks) Build a two-sided 95% confidence interval to assess if it is appropriate to assume that the variances (or variability) of the weights are the same for genetically modified wa- termelons and regular watermelons. For parts (a), (b) and (c), clearly give the steps and state the conclusions