A sample of 160 colleges is taken and the average number of full-time students is found to be 25,476.69. The standard deviation for full-time attendance at ALL colleges is 2,429.83. Assuming that the number of full-time students is normally distributed: a) Construct a 99% confidence interval for average full-time attendance at ALL colleges. b) Using a 5% significance level, test to see whether average full-time attendance is significantly higher than 25,000. c) Assuming that the average full-time attendance is really 25,500, calculate the probability of a Type I error. d) Calculate the power of the test against this alternative? e) What is the probability of a Type I error?