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 all 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 trees 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) Paragraph V BIUA + 30 ep ADS SHIPQuestion 35 (3 points) Indicate whether each of the following statements is true or false. If a statement contains any errors, rewrite the statement with the appropriate corrections. (If a statement is true, you do not need to explain anything.) Note: For each part of this question, you will get either 0 or 1 mark. No part marks will be given. a) The sample correlation r and the population proportion p are both statistics. b) For a given confidence level, in order to make a confidence interval three times narrower, we must take a sample size three times larger. c) We conduct a hypothesis test of Ho: M - 37 vs. Ha: u > 37 for the mean of some variable, and the null hypothesis is rejected at the 1% level of significance. Therefore, the null hypothesis would also be rejected at the 2% level of significance. Paragraph V BIUVA + . .. 30 TAD SHIFT CTRL