4. BMI is obtained as weight (in kg) divided by the square of height (in M2). Adults with BMI over 25 are considered overweight. A trainer at a health club measured the BMI of people who registered for his program this week. Assume that the population is normal. The numbers are given below. 29.4 24.2 25.6 23.6 23.0 22.4 27.4 27.8 a) Construct a 95% condence interval for the mean BMI. b) To nd if newly registered people for the program are overweight on average, conduct an appropriate test using a = 0.05. 0) Suppose that a further study establishes that, in fact, the population BMI is 25.5. What did the test in part (b) lead to? Was it a correct decision? If not, what type of error did this test make? 5. A toxicologist wishes to investigate the relationship between the probability of a developmental defect and the level of a certain acid in the environment. Twenty mg/kg/day of the acid is given to mice during pregnancy, and the malformation rate of the fetuses is observed. a) How large a sample should be chosen to estimate the proportion with 95% error margin of 0.01? Use p = .2. b) A random sample of 400 mice is taken, and 37 mice were found to have malformed fetuses. Construct a 95% condence interval for the population proportion