Juestion 1. Dan a 6-month exercise program increase the total body bone mineral content TBBMC ) of young women ? A team of researchers is planning a study to examine this question . Based on the results of a previous study, they are willing to assume that o = 2 for the percent change in TBBMC over the 6-month period . A change in TTBBMC increase )would be considered important ,and the researchers would like to have a 'easonable chance of detecting a change of 1% or larger based on a sample of 25 subjects and a = 0.05 . . Set up Ho and Ha for this question. . Calculate the Type I error and interpret it in the context of the exercise program. .Set up the appropriate hypothesis test. Suppose in their sample of 25 subjects ,the average change in TBBMC is 0.53 %. 1. What are the chances that you would reject Ho based on the sample data it II is Wiv really 1%? 5. Interpret the power and type II error in the context of this question Question 2. nt sample of 62 subjects had a mean time of 240 minutes to complete a task with a standard deviation of 12.9 minutes . Produce the 95% CI for the true population mean ime to complete the task. What assumptions did you make for your CI to be valid ? Juestion 3. A sample of 12 subjects had a mean time of 56 minutes of restless sleep in one night. Dast studies have shown that the standard deviation is around 15.6 minutes . Produce he 95 % CI for the true population mean time to complete the task. What assumptions iid you make for your CI to be valid ? Question 4. Suppose that in a sample of 130 people ,34 gave a "poor " or "very poor " rating to the 1ew premier. Use the above sample data to obtain a 95% confidence interval for the rue proportion of people who would give a "poor " or "very poor " rating to the new Jremier .What assumptions or requirements are needed to produce this confidence nterval '2