hmwk problem - need help

#1
One day, it suddenly occurs to you that students at Western seem to be taller than the national average, which you know to be 66 inches. To test your insight, you take a random sample of 50 students and discover their mean height is 70.5 inches with a standard deviation of 8.8.

a) With α less than or equal to .05, test the hypotheses of interest. [Z=3.62, reject Ho, western students are significantly taller]

b) If, in fact, the mean height of all Western students is actually 68 inches, what is the probability that your experiment in part 'a' would cause you to incorrectly fail to reject the null hypothesis? [0.5160]

c) If you repeated the experiment with two random samples, one of 30 students and one of 40, what is the probability that with both samples you will correctly conclude that Western students are significantly taller than the National average, if both samples' heights have a standard deviation of 3.5 and the true mean height of all Western students is actually 68 inches (still using α less than or equal to .05)? [0.9092]