d) Suppose that a further study establishes that, in fact, e population mean is 4 hours. Did the test in part (c) make a correct decision? If not, what type of error did it make? 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 25.5 23.6 23.0 22.4 27.4 27.8 a) Construct a 95% confidence interval for the mean BMI. b) To find if newly registered people for the program are overweight on average, conduct an appropriate test using a = 0.05. c) 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% confidence interval for the population proportion. 6. A random sample of size 13 from a normal population is given below. 69 74 75 76 78 79 8 1 83 83 85 86 87 80 a) Someone claimed that 0 = 10. Does this data set support the claim? Test at E1 = 0.05. b) Test if the population mean is 85 using 0'- = 0.05. c) Find the p-value of the test. 7. An airline claims that only 6% of all lost luggage is never found. If, in a sample, 17 of 200 pieces of lost luggage are not found, test the null hypothesis p = 0.06 against the alternative p > 0.05 at the 0.05 level of signicance. Use the 5 step method