The heights of UNC sophomores are approximately normally distributed. The heights in inches of 8 randomly selected sophomores are shown below. Use these heights to find a 95% confidence interval for the average height u of UNC sophomores. Give the endpoints of your interval to one decimal place. 72, 69, 70, 68, 70, 67, 64, 67 a) Use these heights to find a 95% confidence interval for the average height u of UNC sophomores. Give the endpoints of your interval to one decimal place. 95% confidence interval: ( 66.46 X , 70.3 b) Based on your answer to part a), conduct a level a=0.05 test of the hypotheses H: M = 68; He: u # 68. No additional work should be required! O Reject the null hypothesis at a=0.05. O Fail to reject the null hypothesis at a=0.05. c) Using the 8 data points above, conduct a test of following hypotheses at level of significance a=0.05: Ho: M = 67; H : M > 67 Find the sample mean x, the sample standard deviation s, the appropriate t-statistic and p-value. Use Excel when necessary and give all answers to four decimal places. Sample mean = Sample standard deviation = t = P = X