General Statistics Questions

1. 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!

2. Consider a population with μ = 43 and σ = 5.2.
a. Calculate the z-score for anx̅ 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?

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.

4. Based on a survey of 1,000 adults by Greenfield Online and resported in a May 2009 USA Today Snapshot, adults 24 years of age and under spend a weekly average of $35 on fast food. If 200 of the adults surveyed were in the age catetory of 24 and under and they provided a standard deviation of $14.50, construct a 95% confidence interval for the weekly average expenditure on fast food for adults 24 years of age and under. Assume fast food weekly expenditures are normally distributed.

5. An experiment ws designed to estimate the mean difference in weight gain for pigs fed ration A as compared with those fed ration B. Eight pairs of pigs were used. The pigs within each pair were littermates. The rations were assigned at random to the two animals within each pair. The gains (in pounds) after 45 days are shown below:

RationA      RationB
65               58
37               39
40               31
47               45
49               47
65               55
53               59
59               51

Assuming weight gain is normal, find the 95% confidence interval estimate for the mean of the differences μd where d= ration A – ration B.

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