A pharmaceutical company claims 90% success rate of a newly invented drug to treatarthritis pain. To examine the claim, a doctor administered the prescribed dose to 10arthritis patients. She observed Y, the number of participants for which the drug waseffective. A test is defined so as to reject Ho: p = 0.9 in favour of Ha: p < 0.9 bythe rejection region {y < k} where k is a positive integer. Note that p is the populationproportion of arthritis patients for which the drug was effective.(d) Find the power of the test for p = 0.3, 0.5, 0.7, 0.9.(e) Sketch a graph of the power function against p (0 < p ≤ 1), and comment on howthe power changes as p changes. [Hint: You may use Table 1 in Appendix 3 ofWMS.]

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Answered: A pharmaceutical company claims 90%…

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 random sample of 80 poultry farms of one variety gave an average production of 240 eggs per bird. Another random sample of 50 poultry farms of another variety gave an average production of 195 eggs per bird. At a=0.05 is there sufficient evidence to support that there is a significant difference between the egg production of the two varieties of birds. Assume o1 =18 eggs and o2=15 eggs
In a random sample of 1022 Canadian adults, 480 think that the Canadian government is doing too little to protect the environment. In another random sample of 1008 Canadian adults taken 10 years ago, 514 think that the Canadian government is doing too little to protect the environment. At a=0.10, can you reject the claim that the proportion of US adults who think that the Canadian government is doing too little to protect the environment hasn't changed?
A researcher has developed a new drug designed to reduce blood pressure. In an experiment, 22 subjects were assigned randomly to the treatment group and received the new experimental drug. The other 24 subjects were assigned to the control group and received a standard, well-known treatment. After a suitable period, the reduction in blood pressure for each subject was recorded. A summary of these data is: nn x¯x¯ ss Treatment group (new drug) 22 23.48 8.01 Control group (old drug) 24 18.52 7.15 Without using software, how would you estimate the number of degrees of freedom for this problem? Select one: use the larger value, 23, chosen from the two options 21 and 23 use the smaller value, 22, chosen from the two options 22 and 24 use the larger value, 24, chosen from the two options 22 and 24 use the smaller value, 21, chosen from the two options 21 and 23
The following table shows the results of a screening test hypothesized to detect persons at risk for side effects of a new cosmetic surgery. Compute the specificity of the test. Side effects present Side effects absent Screen positive 12 Screen negative 85 204
A sample of 900 commuters from New York were interviewed randomly and 416 answered they like express trains. Determine if the sample evidence shows that less than half of the commuters like express trains. Use α=0.05.
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?
A single sample Z-test is to be done on a study about typhoons. Many believe that the average number of typhoons that enter the Philippines each year is at least 18 (o ≥ 18). Some climatologists, however, observe that the true average number of typhoons that enter the Philippines each year is less than 18. Science teachers from LPU collected the data about the typhoons that entered the country each year since 1900 (n = 32). The sample mean is x = 17. The population with a standard deviation of a = 1.5. The researchers chose to use Single Sample Z-Test. They agreed on a Type I error rate of a = 0.05. 24. State the Null and Alternative Hypotheses. 25. What is the Level of Confidence? 26. What is the critical value?. Hint: You will find it in the standard normal table. 27. What is the decision rule? 28. What is the equivalent z-score of x = 17? A. 1.5 C. 3.0 B. -3.77 D. -1.97 29. What is the conclusion for this problem? 30. In this same problem, how do you state the null hypothesis when…
A research center claims that 31% of adults in a certain country would travel into space on a commercial flight if they could afford it. In a random sample of 800 adults in that country, 33% say that they would travel into space on a commercial flight if they could afford it. At a =0.01, is there enough evidence to reject the research center's claim? Complete parts (a) through (d) below. C No more than % of adults in the country would travel into space on a commercial ight it they could attord it. Let p be the population proportion of successes, where a success is an adult in the country who would travel into space on a commercial flight if they could afford it. State Ho and H Select the correct choice below and fill in the answer boxes to complete your choice. (Round to two decimal places as needed.) OA Ho: ps OB. Ho: p> OC. Ho: p H p= Ha:p> H ps VE Ho: p= 0.31 O D. Ho: p< OF H: p2 H: p2 H p 0.31 (b) Use technology to find the P-value. Identify the standardized test statistic. z= 1.22…
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Your company manufactures plastic wrap for food storage. The tear resistance of the wrap, denoted by X, must be controlled so that the wrap can be torn off the roll without too much effort but it does not tear too easily when in use. In a series of tests (see data table below), 15 rolls of wrap are made under carefully controlled conditions and the tear resistance of each rool is measured. The results are used as the basis of a quality assurance specification. If X for a subsequently produced roll falls more than two standard deviations away from the test period average, the process is declared out of specification and production is suspended for routine maintenance. Roll 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 X 134 131 129 133 135 131 134 130 131 136 129 130 133 130 133 a)What is the mean tear resistance? Enter your answer to the correct number of significant figures. b)What is the…

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