A new treatment for a disease is being tested, to see whether it is better than the standard treatment. The existing treatment is effective on 50% of patients. It is believed initially that there is a 2/3 chance that the new treatment is effective on 75% of patients, and a 1/3 chance that the new treatment is effective on 50% of patients. In a pilot study, the new treatment is given to 20 patients selected at random, and turns out to be effective for 14 of them. What is the probability that the treatment is effective conditional on the results of the study

A new treatment for a disease is being tested, to see whether it is better than the standard treatment. The existing treatment is effective on 50% of patients. It is believed initially that there is a 2/3 chance that the new treatment is effective on 75% of patients, and a 1/3 chance that the new treatment is effective on 50% of patients. In a pilot study, the new treatment is given to 20 patients selected at random, and turns out to be effective for 14 of them. What is the probability that the treatment is effective conditional on the results of the study

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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Two different blood pressure medicines are being compared to determine if the average reduction in blood pressure is the same for each medication. The goal of the study is to determine if the medications differ. Twenty men age 50-60 years old are selected for the study. Ten men are chosen at random to receive the first medication and the other 10 men receive the second medication. Each of the 20 men is monitored for one month to determine the change in blood pressure over that time. Minitab provides the 95% confidence interval for (mu1 - mu2) (2.63, 14.18) a. Interpret this 95% CI. b. What assumptions (be specific) are necessary to construct this CI?
In a randomized, controlled experiment without a placebo, which of the following could cause us to establish a difference between the treatment and the control group? Select an answer and submit. For keyboard navigation, use the up/down arrow keys to select an answer. a A causal relationship between the treatment and the patient's outcome. b The placebo effect. c Random chance causing a statistically significant difference between the control and treatment groups. d All of the above.
When neither the subject nor those having contact with the subject know the treatment assignment, the study is called unbiased. double-blind. blind. statistically significant. randomized.
10.In a study we reject Ho Which of the following statements are incorrect and why? (a) "Now we know that H, is false." (b) "We have proof that our sample mean represents a particular p." (c) "We have proof that the independent variable causes scores to change as predicted." (d) "It is not pos- sible that the difference between X and u is due to sampling error." (e) "We have evidence that the predicted relationship does
A large clinical trial of the effect of diet on breast cancer assigned women at random to either a normal diet or a low-fat diet. To check that the random assignment did produce comparable groups, we can compare the two groups at the start of the study. Asked if there is a family history of breast cancer: 1276 of the 5964 women in the low-fat group and 1507 of the 7726 women in the control group said "Yes." If the random assignment worked well, there should not be a significant difference in the proportions with a family history of breast cancer. How significant is the observed difference? State: Is there evidence of a difference in the proportion of women with a family history of breast cancer between the treatment and control groups? Plan: Let pi be the proportion for the treatment group, and Pz the proportion for the control group. State the hypotheses for your test. Ha:Pi + P2 Solve: Give the value of the test statistic. Use the calculator. Select an answer ♥ Ho:pi = p2 What is the…
In randomized, double-blind clinical trials of a new vaccine, children were randomly divided into two groups. Subjects in group 1 received the new vaccine while subjects in group 2 received a control vaccine. After the second dose, 125 of 746 subjects in the experimental group (group 1) experienced fever as a side effect. After the second dose, 82 of 627 of the subjects in the control group (group 2) experienced fever as a side effect. Does the evidence suggest that a higher proportion of subjects in group 1 experienced fever as a side effect than subjects in group 2 at the a= 0.01 level of significance? Find the test statistic for this hypothesis test. (Round to two decimal places as needed.)
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A teaching assistant for a psychology course is curious about what factors are associated with higher final grades in the course. She finds that students who read the textbook tend to have higher final grades in the course. She finds that students who watch the lecture videos tend to have higher final grades in the course. Lastly, she finds that students who read the textbook and watch the lecture videos tend to have the highest grades in the course. Assuming that any difference is statistically significant, which of the following best characterizes these results? 1 main effect and O interaction effects 1 main effect and 1 interaction effect O main effects and O interaction effects 2 main effects and 1 interaction effect O main effects and 1 interaction effect 2 main effects and O interaction effects
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Dr. Sloane is doing a study to test the association between alcohol consumption and the occurrence of cancer of the liver. He chooses a hospital-based sample and collects all newly diagnosed cases of histologically confirmed liver cancer diagnosed at that hospital. For his control group, he reviews the charts of all patients coming through all the clinics at this hospital who are not diagnosed with liver cancer. He makes sure that the cases and controls are similar by age and sex. A. Looking at the odds ratios and the p-values together, describe your observations. B. Looking at the p-values, what do they tell you about the strength of the association between drinking different amounts of alcohol per day and the risk of having liver cancer?