Using the telephone numbers listed in your local directory as your population, randomly obtain 20 samples of size 3. From each telephone number identified as a source, take the fourth, fifth, and sixth digits. a. Calculate the mean of the 20 samples b. Draw a histogram showing the 20 sample means. (Use classes -0.5 to 0.5, 0.5 to 1.5, 1.5 to 2.5 and so on). c. Describe the distribution of the x-bars that you see in part b (shape of distribution, center, and the amount of dispersion). d. Draw 20 more samples and add the 20 new x-bars to the histogram in part b. Describe the distribution that seems to be developing. Use the empirical rule to test for normality. See the sampling distribution of sample means and the central limit theorem develop from your own data! Question 2 Consider a population with ? = 43 and ? = 5.2. a. Calculate the z-score for an x? of 46.5 from a sample of size 35. b. Could this z-score be used in calculating probabilities using Table 3 in Appendix B? Why or why not? Question 3 State the null and alternative hypotheses for each of the following: a. You want to show an increase in buying and selling of single-family homes this year when compared with last year’s rate. b. You are testing a new recipe for “low-fat” cheesecake and expect to find that its taste is not as good as traditional cheesecake. c. You are trying to show that music lessons have a positive effect on a child’s self-esteem. d. You are investigating the relationship between a person’s gender and the automobile he or she drives—specifically you want to show that more males than females drive truck-type vehicles.