1. The shelf life of a certain ointment is known to have a normal distribution. A sample of size 120 tubes of ointment gives )7 = 36.1 and s = 3.7. a) Construct a 95% condence interval of the population mean shelf life. b) Suppose a researcher believed that before the experiment 0 = 4. What would be the required sample size to estimate the population mean to be within 0.5 months with 99% condence? 2. The foot size of each of 16 men was measured, resulting in the sample mean of 27.32 cm. Assume that the distribution of foot sizes is normal with o = 1.2 cm. a) Test if the population mean of men's foot sizes is 28.0 cm using 01. = 0.01. b) If or. = 0.01 is used, what is the probability of a type II error when the population mean is 27.0 cm? c) Find the sample size required to ensure that the type II error probability 0(27) = 0.1 when on = 0.01. 3. A computer company claims that the batteries in its laptops last 4 hours on average. A consumer report rrn gathered a sample of 16 batteries and conducted tests on this claim. The sample mean was 3 hours 50 minutes, and the sample standard deviation was 20 minutes. Assume that the battery time distribution as normal. a) Test if the average battery time is shorter than 4 hours at or = 0.05. b) Construct a 95% condence interval of the mean battery time. c) If you were to test H0: p. =240 minutes vs. H1: u 75 240 minutes, what would you conclude from your result in part (b)? d) Suppose that a further study establishes that, in fact, the population mean is 4 hours. Did the test in part (c) make a correct decision? If not, what type of error did it make