Answer Happy

6. [14 marks] On a certain day in July, the maximum temperature, mºC, was recorded at 11 points randomly chosen points on the island of Isla Sorna. On the same day, the maximum temperature, p°C, was recorded at 20 randomly chosen points on the island of Isla Nublar. Summary statistics are given below: nm = 11, m = 25.30; ny = 20, p = 26.45 21:(mi – m)2 = 16.74; 2-1(Pi-p)2 = 15.29 We are interested in testing the claim Ho: Um = Mp. = We have been told that the temperatures are Normally distributed. A colleague has told us that we can assume that the underlying population variances are equal. = a. [5] In order to test the claim Ho: Um = Mp, we need to first check to see if what the colleage has told us is reasonable. Check their claim by testing another hypothesis first: Ho: Om = Op = 0. When you calculate the observed value of the test statistic, put the larger sample variance in the numerator, and the smaller sample variance in the denominator, and then calculate the appropriate p-value to test Ho. Is there evidence to suggest that the colleague's information about the equality of the variances was correct? Be sure to show all steps clearly and show all relevant work in your solution (as noted in question 1). b. [5] Now test Ho: Im = Hy by calculating a p-value. Be sure to show all steps clearly in your solution (as noted in question 1). c. [2] Based on the p-value from part b., would you reject He at a threshold value (or level of significance) of 1%. See page 129 of the course notes for guidance. d. [2] Would you expect 0 to lie in a 99% confidence interval for um – Mp? Justify your answer. You do not have to construct a 99% confidence interval for Hm – Up.