In a comparative study of two new drugs, A and B, 325 patients were treated with drug A, and 250 patients were treated with drug B. (The two treatmentgroups were randomly and independently chosen.) It was found that 221 patients were cured using drug A and 197 patients were cured using drug B. Let p, bethe proportion of the population of all patients who are cured using drug A, and let p, be the proportion of the population of all patients who are cured usingdrug B. Find a 90% confidence interval for p, -p,. Then find the lower limit and upper limit of the 90% confidence interval.Carry your intermediate computations to at least three decimal places. Round your responses to at least three decimal places. (If necessary, consult a list offormulas.)Lower limit:?Upper limit:

Answered: Image /qna-images/answer/81eb64fe-9edc-45fa-a4dc-3af9af1ff0da.jpg

Answered: In a comparative study of two new…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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A pharmaceutical company proposed a vaccine that would combat paralytic polio. Two independent random samples were collected from the population. One random sample of 201,229 was given the placebo, and among them 100,910 contracted paralytic polio. The other random sample of 200,745 was given the vaccine, and among them 50,033 people ended up contracting paralytic polio. Let the true proportion of cases of paralytic polio given placebo be p1p1 and the true proportion of cases of paralytic polio given vaccine be p2. Calculate the upper bound of a 95% confidence interval for p1−p2. Round your answer to three decimal places.
In 2022, the CDC reported that 12.5% of U.S. adults currently smoke cigarettes. From the same report, a random sample of 12,405 Ohioans was taken with 2543 being current smokers. Using α = 0.05, test whether the proportion of Ohioans that smoke cigarettes is different than the proportion of U.S. adults
A study was performed to test the effectiveness of a new treatment for migraines. There were 125 patients in the study. Of these, 60 were randomly assigned to receive the standard treatment and 65 to receive the new treatment. All were instructed to take the medication at the onset of their next migraine and to notice if the pain of their migraine felt reduced after half an hour. Fifty patients receiving the new treatment reported reduced pain, compared with only 40 of the patients receiving the standard treatment. The results seem to favor the new treatment, but could the difference just be due to chance? In this problem, consider the null hypothesis that the percentage of patients with a reduction in pain is the same between the two treatments, versus the alternative hypothesis that the percentages are different. (a) Under the null hypothesis, the difference in the sample percentages is expected to be ___%. The standard error for the difference is estimated to be ___%. (b) Calculate…
Twenty middle-aged men with glucose readings between 90 milligrams per deciliter and 120 milligrams per deciliter of blood were selected randomly from the population of similar male patients at a large local hospital. Ten of the 20 men were assigned randomly to group A and received a placebo. The other 10 men were assigned to group B and received a new glucose drug. After two months, posttreatment glucose readings were taken for all 20 men and were compared with pretreatment readings. The reduction in glucose level (Pretreatment reading − Posttreatment reading) for each man in the study is shown here. Group A (placebo) reduction (in milligrams per deciliter): 12, 8, 17, 7, 20, 2, 5, 9, 12, 6 Group B (glucose drug) reduction (in milligrams per deciliter): 29, 31, 13, 19, 21, 5, 24, 12, 8, 21 Part A: Do the data provide convincing evidence, at the α = 0.02 level, that the glucose drug is effective in producing a reduction in mean glucose level? Part B: Create and interpret a 98%…
In a randomized clinical trial, 888 people were placed given Drug A and 930 were given Drug B. The researcher's goals were to determine which drug had better efficacy against T.B. Of those who were given Drug A, 300 contracted T.B. Of the subjects who were given Drug B, 500 contracted T.B. Calculate and interpret the risk ratio of Drug B compared to Drug A for getting T.B.? 10. In Box City, an influenza vaccine was tested on 1,000 people, 400 males and 600 females. Of the males, 50% contracted influenza after vaccination versus 30% of the females. Calculate and interpret the risk ratio of females compared to males of contracting influenza. 11.
The Office of the University Registrar of Seoul University would like to know if the degree programs in College of Science and Math are equally preferred by students. Furthermore, the office would like to know if such degree programs are related to the gender of the students. The test claim that the proportions of the students enrolled are equal in each degree program at alpha=0.05 Using the data on the number of currently enrolled students in each gender (M of F) in each of the four degree programs, find the: a. Table showing the observed and expected values b. Chi-square critical Value c. Chi-square test statistic d. Accept or Reject the null hypothesis?
Public relation companies conducted two surveys about deodorants. The first survey asked a random sample of 500 men about their use of a natural deodorant. A second survey asked the same questions to a random sample of 550 women. In these two studies, 68% of men and 44% of women stated they were dissatisfied with the effectiveness of natural deodorants. Use these results to answer the following questions about the proportion of men and women's satisfaction with natural deoderants. (Round to the nearest whole person as needed). For the men, the number of success within the sample is . For the U.S. teens, the number of failures within the sample is . For the women, the number of success within the sample is . for the Canadian teens, the number of failures within the sample is .
A pharmaceutical company has developed a drug that is expected to reduce hunger. To test the drug, three samples of rats are selected with n=9 in each sample.The first sample receives the drug every day. The second sample is given the drug once a week, and the third sample receives no drug at all (the control group). These assignments of drugs are called treatments.The (dependent) variable being compared is the amount of food eaten by each rat over a 1-month period. These data are analyzed by an ANOVA, and the results are reported in the following summary table. How many groups (or population means or treatments) are being compared in this problem? _________ (Enter a whole number) What is the total number of data used in this problem? _________(Enter a whole number) Fill in all missing values in the table. (Hint: Start with the df column and your above answers.)If there are decimal places in your answer, provide 2 or more decimal places. Source of Variation SS df MS F…
A cat-lover claims that cats are just as smart as dogs. In order to back this claim up with some evidence she organizes a study at a large local pet daycare center. A random sample of 40 cats are selected and a random sample of 40 dogs are selected. Each of the selected animals is given one hour with a trainer in which the trainer attempts to teach them to roll over. Upon conclusion of the training, the proportion of dogs and proportion of cats that have learned this skill is computed. The trainer reports that she is 90% confident that the true difference in the proportion of all dogs and all cats (pD – pC) that can learn this skill with one hour of training is between –0.05 to 0.28. Which of the following conclusions can be made based upon this confidence interval? (A) Because most of the values in the confidence interval are positive, this proves that dogs are smarter than cats. (B) Because the point estimate of the confidence interval is positive, there is convincing evidence…
The authors of a paper compared two different methods for measuring body fat percentage. One method uses ultrasound, and the other method uses X-ray technology. The table gives body fat percentages for 16 athletes using each of these methods (a subset of the data given in a graph that appeared in the paper). For purposes of this exercise, you can assume that the 16 athletes who participated in this study are representative of the population of athletes. Athlete 0 Ho: Md = Ha: Md 0 < 0 5 6 7 8 9 10 11 12 13 14 15 16 X-ray 4.75 7.00 9.25 12.00 17.25 29.50 5.50 6.00 8.00 8.50 9.25 11.00 12.00 14.00 17.00 18.00 USE SALT Ultrasound 4.75 4.00 9.00 11.75 17.00 27.75 6.50 6.75 8.75 9.75 9.50 12.00 12.25 15.75 18.00 18.50 X Find the test statistic and P-value. (Use a table or SALT. Round your test statistic to one decimal place and your P-value to three decimal places.) t = P-value = 0.000 Mx-ray ultrasound.)
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…

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