Question 3 [2.5 marks] (a) [1 mark] Given the following statistics, test at the 5% level of significance to determine whether differences exist among the population means using the F-statistic. Assume independent samples from 3 populations, the unknown population variances are equal (of = 0? = 03), and all 3 populations are normally distributed. n1 =5 n2 = 5 n3 = 5 X1 = 10 X2 = 15 X3 = 20 S1 = 5 $2 = 5 83 = 5 (b) [1 mark] Repeat part (a), changing all three sample means to 10; that is 1 = 10 2 = 10 3 = 10 (c) [0.5 marks] Are you surprised that the result of the hypothesis testing in part (b) is that we fail to reject the null hypothesis? Why or why not