sugar concentration

3. An article in Food Testing and Analysis, “Improving Reproducibility of Refractometry Measurements of Fruit Juices” (1999, V4, pp 13-17) measured the sugar concentration (Brix) in clear apple juice. All readings were taken at 20oC:

11.48
11.50
11.45
11.42
11.48
11.49
11.47
11.45
11.48
11.44
11.45
11.50
11.47
11.49
11.46
11.45
11.47
11.46
11.43
11.47

a. The research team was interested in finding if the true mean concentration is 11.5 at a level of significance of a =0.05. Using the P-value determine the conclusion of the research team about the mean concentration. Clearly state your null and alternative hypothesis.
b. Compute the power of the test if the true mean is 11.4.
c. What sample size would be required to detect a true mean sugar concentration of 11.45 if we wanted the power of test to be at least 0.9?
d. Explain and calculate how question in part (a) could be answered by constructing the appropriate confidence interval on the mean sugar concentration.