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# ANOVA and Regression problems

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1. A research study is documenting the results of an investigation weight loss medication on eight overweight adult males, according to body mass index. Their pre-treatment weight is recorded and compared against their post-treatment weight four weeks later.
Pre-Treatment: 185 174 160 225 191 200 172 175
Post-Treatment: 180 167 150 217 182 194 160 160

Is the post-treatment weight significantly less than the pre-treatment weight for these adult males, at the 0.005 level of significance? [COMMENTS & HINTS: Compare post-test minus pre-test, hence obtaining a negative difference for a left tail test. Are the pairs of data independent? No!]

2. The office manager of a medical office with two physicians wonders if there is any difference in the mean number of patients seen by each doctor during morning office hours on any given night. The first, Dr. Quincy, examines a mean average of 14 patients, with a sample standard deviation of 4 patients, based on a random sample of nine mornings; the second, Dr. Quinn, examines a mean average of 18 patients, with a sample standard deviation of 5 patients, based on a random sample of 16 mornings. Test the claim at the 10% level of significance. [COMMENTS & HINTS: The population standard deviations for both are unknown; do not make any presumptions about them.]

4. The manager of a retail chain of out-patient lab clinic that specializes in hematological draws is comparing the number of patients serviced at three randomly selected stores. The number of patients seen on randomly selected Saturday mornings is as follows:
A 23 36 31 32 40 42 35 40 36 38
B 30 27 24 20 25 16 21 27
C 24 29 35 21 20 30 14

With 95% confidence in the results, are the mean numbers of patients seen comparable at all three stores?

5. During clinical trials, two competing antibiotics were tested to see if they eliminated infections with same proportion of effectiveness in one treatment. With the first medicine, 36 out of 45 were successfully treated; with the second medicine, 14 out of 35 were successfully treated. At the 5% level of significance, is there any difference in the proportions of effectiveness for the two antibiotics? [COMMENTS & HINTS: Use a pooled proportion.]