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 heightof UNC sophomores. Give the endpoints of your interval to one decimal place.72, 69, 70, 68, 70, 64, 64, 73a) Use these heights to find a 95% confidence interval for the average heightof UNC sophomores. Give the endpoints of your interval to one decimal place.95% confidence interval: ( , )b) Based on your answer to part a), conduct a level=0.05 test of the hypotheses

H₀:= 68;H_a:68

. No additional work should be required!Reject the null hypothesis at=0.05.Fail to reject the null hypothesis at=0.05. c) Using the 8 data points above, conduct a test of following hypotheses at level of significance=0.05:

H₀:= 67;H_a:> 67

Find the sample meanx, 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

=