T. The Stanford-Binet IQ test has results that are normally distributed with a mean of 100. A principal in an elementary school believes that her students have above average intelligence and wants verification of her belief. She randomly selects 20 students and checks the student files. She finds the following IO, scores for these 20 students. IQ scores: 110,132, 93, 97, 115, 145, 77, 130, 114, 123, 39, 101, 92, 85, 112, 79, 139, 102, 103, 89 a. Compute the sample mean and sample standard deviation of the \"15 of the students sampled. Round to 1 decimal place. (4 pts.) b. Construct a 95% confidence interval for the mean IQ of students at this school. Show all steps in the computation of the error and the interval endpoints. Round to 1 decimal place. (10 pts.) c. The confidence interval has a fairly large margin of error due to the small sample size. Suppose the principal wanted to estimate the mean IQ of her students with 95% confidence and with a margin of error of 1.5 points. Using the value of s from part (a), what sample size would be required? (3 pts.) In a study of middle-aged Finnish men, the researchers were interested in determining whether there was a relationship between coffee consumption and white blood cell count. The white blood cell count of 77 non-coffee drinkers was compared to the white blood cell count of 351 heavy coffee drinkers. "Heavy\" coffee drinking was dened as an average of 960 ml of coffee per day. The study reported that for non-coffee drinkers, the mean blood oell count was 5.2 with a standard deviation of 1.4. For the heavy coffee drinkers, the mean blood cell count was 6.0 with a standard deviation of 1.7. The blood cell counts were measured in billions per liter. Is there sufficient evidence to conclude that the mean blood cell count of heavy coffee drinkers is higher than the mean blood cell count of non-coffee drinkers? Use a level of signicance of .05. Show all 6 steps in the hypothesis test. (16 pts.)