Please help me answer PRACTICE EXERCISE with SOLUTION

10. A random sample of size 8 drawn from a normal population yielded the following results: x - 289, s = 46. Test H : J = 250 vs. H : u > 250 at a = 0.05. 11. Researchers wish to test the efficacy of a program intended to reduce the length of labor in childbirth. The accepted mean labor time in the birth of a first child is 15.3 hours. The mean length of the labors of 13 first-time mothers in a pilot program was 8.8 hours with a standard deviation of 3.1 hours. Assuming a normal distribution of times of labor, test at 10% level of significance test whether the mean labor time for all women following this program is less than 15.3 hours. 12. Six coins of the same type are discovered at an archaeological site. If their weights on the average are significantly different from 5.25 grams then it can be assumed that their provenance is not the site itself. The coins are weighed and have a mean of 4.73 g with a sample standard deviation of 0.18 g. Perform the relevant test at the 0.1% (th of 1% level of significance, assuming a normal distribution of weights of all such coins. 13. The recommended daily allowance of iron for females aged 19 - 50 is 18 mg/day. A careful measurement of the daily iron intake of 15 women yielded a mean daily intake of 16.2 mg with sample standard deviation 4.7 mg. a. Assuming that daily iron intake in women is normally distributed, perform the test that the actual mean daily intake for all women is different from 18 mg/day, at 10% level of significance. b. The sample mean is less than 18, suggesting that the actual population mean is less than 18 mg/day. Perform this test, also at 10% level of significance. (The computation of the test statistic done in part (a) still applies here.) 14. The average number of days to complete recovery from a particular type of knee operation is 123.7 days. From his experience a physician suspects that the use of a topical pain medication might be lengthening the recovery time. He randomly selects the records of seven knee surgery patients who used the topical medication. The times to total recovery were: 128 135 121 142 126 151 123 a. Assuming a normal distribution of recovery times, perform the relevant test of hypotheses at 10% level of significance. b. Would the decision be the same at 5% level of significance? Answer either by constructing a new rejection region. 15. Pasteurized milk may not have a standardized plate count (SPC) above 20,000 colony- forming bacteria per milliliter (cfu/ml). The mean SPC for five samples was 21,500 cfu/ml with a sample standard deviation of 750 cfu/ml. Test the null hypothesis that the mean SPC for this milk is 20,000 versus the alternative that it is greater than 20,000, at 10% level of significance. Assume that the SPC follows a normal distribution. 143Step 5: As shown in Figure 5.9 the test statistic does not fall in the rejection region. The decision is not to reject H. In the context of the problem our conclusion is: HM # 0.02 The data do not provide sufficient evidence, at 1% level of significance, to 2= 0.005 " = 0.005 conclude that the mean distance between the holes in the component differs 0 -17 =-5.841 t- = 5.841 from 0.02 mm. Reject H 0 Reject H T = 0.877 Figure 5.9 Practice Exercises 5.3 A. Find the rejection region (for the standardized test statistic) for each hypothesis test based on the given information. The population is normally distributed. 1. H : H= 27 vs. H. : u -105 at a = 0.10, n = 24, o unknown. 4. H : M = 78.8 vs. H, : u # 78.8 at a = 0.10, n = 8, 0 = 1.7. B. Find the rejection region (for the standardized test statistic) for each hypothesis test based on the information given. The population is normally distributed. Identify the test as left-tailed, right-tailed, or two-tailed. 5. H : M= 14 vs. H : u 3.8 at a = 0.001, n = 27, o-unknown. C. Solve the following problems: 9. A random sample of size 20 drawn from a normal population yielded the following results: x = 49.2, s = 1.33. Test Ho : M = 50 vs. H. : u # 50 at a = 0.01. 142 STATISTICS AND PROBABILITY