Two drugs, A and B, were tested on a total of 2000 patients, half of whom were women and half of whom were men. Drug A was given to 900 patients, and Drug B to 1100 patients. The results are presented in the table below. Women Men Drug A 5 of 100 cured 400 of 800 cured Drug B 101 of 900 cured 196 of 200 cured
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Two drugs, A and B, were tested on a total of 2000 patients, half of whom were women and half of whom were men. Drug A was given to 900 patients, and Drug B to 1100 patients. The results are presented in the table below.
Women Men Drug A 5 of 100 cured 400 of 800 cured Drug B 101 of 900 cured 196 of 200 cured -
Give numerical evidence to support the claim that Drug B is more effective than Drug A.
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Give numerical evidence to support the claim that Drug A is more effective than Drug B.
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Which claim do you think makes more sense? Why?
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- 2. Suppose that in Example 2.27, 400 units of food A, 500 units of B, and 600 units of C are placed in the test tube each day and the data on daily food consumption by the bacteria (in units per day) are as shown in Table 2.7. How many bacteria of each strain can coexist in the test tube and consume all of the food? Table 2.7 Bacteria Strain I Bacteria Strain II Bacteria Strain III Food A 1 2 0 Food B 2 1 3 Food C 1 1 1A company claims that its brand of dish detergent, A, is more effective than a competitor’s brand, B. Fifty dirty dishes are randomly selected and randomly divided into two groups. In one group, each dirty dish will be placed in a container of hot water with Brand A detergent and in the other group, each dirty dish will be placed in a container of hot water with Brand B detergent. The dishes will sit for two hours, and then the cleanliness of the dishes will be measured using a scale of 1–10 (1 = least clean to 10 = most clean). The difference in mean cleanliness ratings for the two detergents (A – B) will then be calculated. What is the appropriate inference procedure?A laundry detergent company wants to determine if a new formula of detergent, A, cleans better than the original formula, B. Researchers randomly assign 500 pieces of similarly soiled clothes to the two detergents, putting 250 pieces in each group. After washing the clothes, independent reviewers determine the cleanliness of the clothes on a scale of 1–10, with 10 being the cleanest. The researchers calculate the proportion of clothes in each group that receive a rating of 7 or higher. For detergent A, 228 pieces of clothing received a 7 or higher. For detergent B, 210 pieces of clothing received a rating of 7 or higher. Assuming the conditions for inference are met, what is the 90% confidence interval for the difference in proportions of clothes that receive a rating of 7 or higher for the two detergents?
- A laundry detergent company wants to determine if a new formula of detergent, A, cleans better than the original formula, B. Researchers randomly assign 500 pieces of similarly soiled clothes to the two detergents, putting 250 pieces in each group. After washing the clothes, independent reviewers determine the cleanliness of the clothes on a scale of 1–10, with 10 being the cleanest. The researchers calculate the proportion of clothes in each group that receive a rating of 7 or higher. For detergent A, 228 pieces of clothing received a 7 or higher. For detergent B, 210 pieces of clothing received a rating of 7 or higher. Assuming the conditions for inference are met, what is the 90% confidence interval for the difference in proportions of clothes that receive a rating of 7 or higher for the two detergents? Find the z-table here.A laundry detergent company wants to determine if a new formula of detergent, A, cleans better than the original formula, B. Researchers randomly assign 500 pieces of similarly soiled clothes to the two detergents, putting 250 pieces in each group. After washing the clothes, independent reviewers determine the cleanliness of the clothes on a scale of 1–10, with 10 being the cleanest. The researchers calculate the proportion of clothes in each group that receive a rating of 7 or higher. For detergent A, 228 pieces of clothing received a 7 or higher. For detergent B, 210 pieces of clothing received a rating of 7 or higher. Based on the 90% confidence interval, (0.02, 0.12), is there convincing evidence that the new formula of laundry detergent is better? A) There is convincing evidence because the interval is entirely above 0. B) There is not convincing evidence because the sample sizes are too small. C) There is convincing evidence because the number of clothing items receiving a…To determine the effectiveness of an oil additive, a testing firm purchased two cars of the same make, year, and model, and drove each a distance of 30,000 miles using the same kind of gasoline, the same kind of oil, the same driver, under the same road conditions. The oil in one engine included the additive, whereas the oil in the other engine did not. At the end of the test, the engines of both cars were dismantled, and it was found that the engine that contained the additive had less wear. The testing firm concluded that the oil additive caused the reduced wear.
- A producer of pocket calculators purchases the main processor chips in lots of1,000. The producer would like to have a 1 percent rate of defectives but willnormally not refuse a lot unless it has 4 percent or more defectives. Samples of50 are drawn from each lot, and the lot is rejected if more than two defectives arefound.a. What are p0, p1, n, and c for this problem?In order to determine whether a particular medication was effective in curing the common cold, one group of patients was given the medication, while another group received sugar pills. The results of the study are shown below. PatientsCured PatientsNot Cured Received medication 70 10 Received sugar pills 20 50 We are interested in determining whether the medication was effective in curing the common cold.Independent studies show that 26 out of 40 r/s full-time students favor a shorter semester system, while 38 out of 50 r/s part-time students favor the same. Construct a 98% c.i. for the difference between the overall percentage of full-time students favoring a shorter semester system and that of part-time students.
- You are the newly appointed assistant administrator at a local hospital, and your first project is to investigate the quality of the patient meals put out by the food-service department. You conducted a 10-day survey by submitting a simple questionnaire to the 400 patients with each meal, asking that they simply check off that the meal was either satisfactory or unsatisfactory. For simplicity in this problem, assume that the response was 1,000 returned questionnaires from the 1,200 meals each day. The results are as follows: Day Number of Unsatisfactory Meals 1-Dec 74 2-Dec 42 3-Dec 64 4-Dec 80 5-Dec 40 6-Dec 50 7-Dec 65 8-Dec 70 9-Dec 40 10-Dec 75 a. Construct an appropriate control chart based on the questionnaire results, using two-sigma control limits. b. What comments can you make about the results of the survey? c. Show breakdown of computation/work.In a comparative study of two new drugs, A and B, 350 patients were treated with drug A, and 225 patients were treated with drug B. (The two treatment groups were randomly and independently chosen.) It was found that 241 patients were cured using drug A and 157 patients were cured using drug B. Let p1 be the proportion of the population of all patients who are cured using drug A, and let p2 be the proportion of the population of all patients who are cured using drug B. Find a 90% confidence interval for −p1p2 . Then complete the table below. Carry your intermediate computations to at least three decimal places. Round your responses to at least three decimal places. (If necessary, consult a list of formulas.) What is the lower limit of the 90% confidence interval? What is the upper limit of the 90% confidence interval?Consider the hypothetical case that there were only two brands of juice on the market, company A and company B. 52% of the population drinks juice from company A (it is not known whether these people consume only juice A or if they also consume juice B). 51% of the population drinks juice of company B (again, it is not known how many of these people drink only juice B or if they drink both juice). However, it is known that 21% of the population does not drink juice. Based on these data, we can estimate that the percentage of the population that drinks juice from both companies is: (choose only one): a) 36% b)37% c) 24% d)23% e)5.3%