the following questions. Show all work. If you use StatKey, Minitab Express, you must include the appropriate output (copy + paste) along with an explanation. Round all answers to at least 3 decimal places. 1. A test prep company has developed a new intervention to improve SAT-Verbal scores. They will conduct a hypothesis test to determine if the average SAT-Verbal score of a student who has completed their program is greater than the known national average of 509. The program is very expensive at $22,000 per student. Use this scenario to answer the following questions. [50 points] A. Write out the null and alternative hypotheses using the appropriate symbols. For a review of using the equation editor in Word, see https://onlinecourses.science.psu.edu/statprogram/equations B. In terms of this scenario, describe what a Type I error would look like. (Be sure to apply this scenario!) C. In terms of this scenario, describe what a Type II error would look like. (Be sure to apply this scenario!) D. The researchers used a sample size of n= 9,000 and found a sample mean of 513. Using your hypotheses from part A, and the known population standard deviation of 100, what is the test statistic? You may do hand calculations or use Minitab Express (https://onlinecourses.science.psu.edu/stat200/node/228) E. What is the p-value associated with the test statistic you computed in part D? F. Are the results of this study statistically significant? Explain why. G. Are the results of this study practically significant? For example, if you were a parent, would you be convinced that you should spend $12,000 to send your child through this program? Explain why. H. Rerun the analyses from part D using a sample size of n=35. Use the five-step hypothesis testing procedure. Step 1: Step 2: Step 3: Step 4: Step 5: I. How did decreasing the sample size from 9,000 to 35 change the statistical power of this test? 2. Answer the following questions using the dataset Spring17StData.MTW. Consider this data to be a sample that is representative of the population of all Penn State World Campus STAT 200 students. [50 points] A. At the .05 alpha level, is there evidence that the mean height of all Penn State World Campus STAT 200 students is greater than 65 inches? Use the five-step hypothesis testing procedure. Step 1: Step 2: Step 3: Step 4: Step 5: B. In part A, is it possible that a Type I or Type II error was committed? Explain Why. C. At the .05 alpha level, is there evidence that the proportion of females in the population of all Penn State World Campus STAT 200 students is different from 50%? Use the five-step hypothesis testing procedure. Use the normal approximation method if appropriate. Step 1: Step 2: Step 3: Step 4: Step 5: D. Construct a 95% confidence interval for the proportion of the population that owns wearable technology. Use the normal approximation method if appropriate. E. At the .05 alpha level, is there evidence that the proportion of this population that owns wearable technology is different from 50%? Assume that in the population this variable is normally distributed. Use the five-step hypothesis testing procedure. Use the normal approximation method if appropriate. Step 1: Step 2: Step 3: Step 4: Step 5: F. Compare your results from part D and part E. 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