From a population with standard deviation 25, a sample of size 100 is drawn. The mean of the sample is 235. Construct a 90% confidence interval for...

1. From a population with standard deviation 25, a sample of size 100 is drawn. The mean of the sample is 235. Construct a 90% confidence interval for the true mean of the population.

2. Joey says that 90% of the observations are in this interval. Is Joey right? If not, what is the proper interpretation of this 90% confidence interval?

3. An evaluator wishes to make a statement about the emotional maturity of the freshmen population, so she decides to sample the population and administer an emotional maturity test. Putting aside any concerns about the validity of the test used, and considering the sample techniques only, how many students should she sample in order to be 95% confident that her estimate of freshman emotional maturity will be within 6 units of the true mean? (The test publishers indicate that the population variance is 100 units.)