Authors of a computer algebra system wish to compare the speed of a new computational algorithm to the currently implemented algorithm. They apply the new algorithm to 50 standard problems; it averages
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Authors of a computer algebra system wish to compare the speed of a new computational algorithm to the currently implemented algorithm. They apply the new algorithm to 50 standard problems; it averages 8.16 seconds with standard deviation 0.17 second. The current algorithm averages 8.22 seconds on such problems. Test, at the 1% level of significance, the alternative hypothesis that the new algorithm has a lower average time than the current algorithm.
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- The University is considering changing the email system that they currently use. Since there are substantial learning costs associated with any new software, the University only wants to change to the new system if it is very confident that there is at least a 20% difference in the proportion of faculty and staff who say they like the new system. In a sample of 120 users of the current system, the University finds that 65 say they like the current system. In another sample of 90 experimental users of the “new” system, the University finds that 70 of them like the new system. When testing the hypothesis (using a 5% level of significance) that there is at least a 20% difference in the proportion of users who like the two systems, the p-value is .2943; what is your conclusion concerning the null hypothesis? Reject the null hypothesis Fail to reject the null hypothesisThe University is considering changing the email system that they currently use. Since there are substantial learning costs associated with any new software, the University only wants to change to the new system if it is very confident that there is at least a 20% difference in the proportion of faculty and staff who say they like the new system. In a sample of 140 users of the current system, the University finds that 75 say they like the current system. In another sample of 85 experimental users of the “new” system, the University finds that 72 of them like the new system. When testing the hypothesis (using a 5% level of significance) that there is at least a 20% difference in the proportion of users who like the two systems, what is the null and alternative hypothesis?The University is considering changing the email system that they currently use. Since there are substantial learning costs associated with any new software, the University only wants to change to the new system if it is very confident that there is at least a 20% difference in the proportion of faculty and staff who say they like the new system. In a sample of 131 users of the current system, the University finds that 66 say they like the current system. In another sample of 91 experimental users of the “new” system, the University finds that 75 of them like the new system. When testing the hypothesis (using a 5% level of significance) that there is at least a 20% difference in the proportion of users who like the two systems, what is the test statistic? (please round your answer to 2 decimal places)
- Although there is a popular belief that herbalremedies such as Ginkgo biloba and Ginseng mayimprove learning and memory in healthy adults,these effects are usually not supported by wellcontrolled research (Persson, Bringlov, Nilsson,and Nyberg, 2004). In a typical study, a researcherobtains a sample of n = 16 participants and has eachperson take the herbal supplements every day for90 days. At the end of the 90 days, each person takesa standardized memory test. For the general population, scores from the test form a normal distributionwith a mean of μ = 50 and a standard deviation ofσ = 12. The sample of research participants had anaverage of M = 54.a. Assuming a two-tailed test, state the null hypothesis in a sentence that includes the two variablesbeing examined.b. Using the standard 4-step procedure, conduct atwo-tailed hypothesis test with α = .05 to evaluatethe effect of the supplements.The dataset TrafficFlow gives the delay time in seconds for 24 simulation runs in Dresden, Germany, comparing the current timed traffic light system on each run to a proposed flexible traffic light system in which lights communicate traffic flow information to neighboring lights. On average, public transportation was delayed 105 seconds under the timed system and 44 seconds under the flexible system. Since this is a matched pairs experiment, we are interested in the difference in times between the two methods for each of the n=24 simulations. For the differences D, we were given that seconds with seconds. We wish to estimate the average time savings for public transportation on this stretch of road if the city of Dresden moves to the new system.The standard error is 3.1 for one set of 10,000 bootstrap samples. Find a confidence interval for the average time savings.Round your answers to one decimal place.how to design the propensity rates of this set of equations to apply it to the gillespie algorithm
- Suppose that in manufacturing a very sensitive electronic component, a company and its customers have tolerated a 2% defective rate. Recently, however, several customers have been complaining that there seem to be more defectives than in the past. Given that the company has made recent modifications to its manufacturing process, it is wondering if in fact the defective rate has increased from 2%. For quality assurance purposes, you decide to randomly select 1,000 of these electronic components before they are shipped to customers. Of the 1,000 components, you find 25 that are defective. Assume that the company produces a very large number of these components on any given day. Set up an appropriate hypothesis to test whether or not the defect rate has increased. Before proceeding to test your hypothesis, check that all assumptions and conditions are satisfied for such a test. Conduct the test using a .05 level of significance (alpha) and state your decision about…Suppose that in manufacturing a very sensitive electronic component, a company and its customers have tolerated a 2% defective rate. Recently, however, several customers have been complaining that there seem to be more defectives than in the past. Given that the company has made recent modifications to its manufacturing process, it is wondering if in fact the defective rate has increased from 2%. For quality assurance purposes, you decide to randomly select 1,000 of these electronic components before they are shipped to customers. Of the 1,000 components, you find 25 that are defective. Assume that the company produces a very large number of these components on any given day. Conduct the test using a .05 level of significance (alpha) and state your decision about whether or not you believe that the defect rate has increased. What would be the minimum number of defectives in a random sample of 1,000 would you need to find in order to statistically decide that the defect…A systems analyst tests a new algorithm designed to work faster than the currently-used algorithm. Each algorithm is applied to a group of 38 sample problems. The new algorithm completes the sample problems with a mean time of 22.07 hours. The current algorithm completes the sample problems with a mean time of 22.33 hours. Assume the population standard deviation for the new algorithm is 4.674 hours, while the current algorithm has a population standard deviation of 5.185 hours. Conduct a hypothesis test at the 0.05 level of significance of the claim that the new algorithm has a lower mean completion time than the current algorithm. Let ?1be the true mean completion time for the new algorithm and ?2 be the true mean completion time for the current algorithm. Pay attention to spaces between words. H0: Ha: z-Test Statistic (round to two decimal places) = p-value (round to four decimal places) = Conclusion (write "R" for reject H0, and "F" for fail to reject H0):
- A systems analyst tests a new algorithm designed to work faster than the currently-used algorithm. Each algorithm is applied to a group of 49 sample problems. The new algorithm completes the sample problems with a mean time of 11.01 hours. The current algorithm completes the sample problems with a mean time of 13.24 hours. The standard deviation is found to be 3.328 hours for the new algorithm, and 3.877 hours for the current algorithm. Conduct a hypothesis test at the 0.05 level of significance of the claim that the new algorithm has a lower mean completion time than the current algorithm. Let μ1μ1 be the true mean completion time for the new algorithm and μ2μ2 be the true mean completion time for the current algorithm. Step 1 of 4 : State the null and alternative hypotheses for the test.The MAKSI FEB UI program is considering buying a copier machine among 5 (five) types, namely the FC1, FC2, FC3, FC4 and FC5 types, where each type has different efficiency in terms of the speed of the number of pages (sheets) copied in one minute. Six staff members conducted an experiment to run each type of copier. The following data shows the number of copied pages (sheets) that can be produced in one minute according to the type of copier, 1 trial, and according to the staff assigned to run each type of copier: FC1 FC2 FC3 FC4 FC5 Staff 1 60 50 63 60 64 Staff 2 56 55 65 58 60 Staff 3 54 56 65 56 58 Staff 4 56 57 67 65 60 Staff 5 54 56 65 60 60 Staff 6 55 52 58 60 55 Some of the results of the calculation of the sum of squares (sum-square) and the average squared (mean square) required for the ANOVA test are provided in the following table: Source of Variation SS Df MS Fstat FTable CopierMachine 333.33 ……… ……… ……… ……… Staff ……….. ……… ……… ……… ……… Error 129.47 ……… ……… Total 532.67 …………Adding computerized medical images to a database promises to provide great resources for physicians. However, there are other methods of obtaining such information, so the issue of efficiency of access needs to be investigated. An article reported on an experiment in which 13 computer-proficient medical professionals were timed both while retrieving an image from a library of slides and while retrieving the same image from a computer database with a Web front end. Subject 1 2 3 4 5 6 7 8 9 10 11 12 13 Slide 31 34 40 25 20 29 35 63 40 51 26 41 32 Digital 24 15 16 14 10 19 6 15 15 12 10 18 18 Difference 7 19 24 11 10 10 29 48 25 39 16 23 14 Estimate the difference between true average times for the two types of retrieval in a way that conveys information about precision and reliability. (Use μslide − μdigital. Use a 95% confidence level. Round your answers to two decimal places.) ( _ , _ )