Question 36 (5 points) Heights of trees at a Christmas tree lot follow a normal distribution with standard deviation 32 cm. A random sample of 8 trees was selected and it was found that they had a mean height of 225 cm. (a) Conduct a hypothesis test at the 2% level of significance to determine whether the true mean height of all Christmas trees on the lot differs from 210 cm. Show al of your steps, including the hypotheses, the calculation of the test statistic and the P-value, and a properly worded conclusion. (4 marks) (b) Based on the data, a 98% confidence interval for the true mean height of all tree on the lot is calculated to be (198.7, 251.3). Could this confidence interval have been used to conduct the test in (a)? Why or why not? If it could have been used, what would the conclusion be, and why? (1 mark)