Answer the following questions using the dataset SP16STUDENTDATA.MTW Consider this data to be a sample that is representative of the population of all Penn State World Campus STAT 200 students. (55 points) A. At the .05 alpha level, is there evidence that the proportion of all World Campus STAT200 students who are dieting is different from 30%? Use the five-step hypothesis testing procedure. B. In part (a), is it possible that a Type I or Type II error was committed? Why? C. At the .05 alpha level, is there evidence that more than 30% of Penn State World Campus STAT 200 students have a cat? Use the five-step hypothesis testing procedure. D. Construct a 95% confidence interval for the population mean of the variable ideal marriage age. Assume that in the population this variable is normally distributed. E. At the .05 alpha level, is there evidence that the mean ideal marriage age is different from 28? Assume that in the population this variable is normally distributed. Use the five-step hypothesis testing procedure. F. Compare your results from part (D) and part (E). Explain how these two results could be used to answer the same research question. G. In terms of the scenario in part (E), explain each of the following changes would impact power: Increase in sample size Change in alpha from .05 to .15 Decrease in sample mean Decrease in sample standard deviation