An experiment was conducted to compare the performance of two potato peelers, and inparticular to discover whether the typical user might be able to peel potatoes faster with onerather than the other. Ten volunteers were used, and each was given both peelers for a periodbefore the experiment in order to gain familiarity with them. In the experiment the volunteersubjects used both peelers on standardised amounts of potatoes, and then repeated theexperiment with the peelers used in the opposite order, so as to eliminate any effect due toordering. The table below gives, for each subject, the mean of the natural logarithms of time(in seconds) needed to complete the tasks.PeelerSubjectAв2:332-3422-76 2-791.912-6231.9142-6052.012-031.771-801-812.001-8181.9991.971.98102.262-30Use Student's t-test, at the 5% level of significance, to test whether the peelers differ in theirefficiency.

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Answered: An experiment was conducted to compare…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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A study was done comparing the effectiveness of exercise vs medication on loweringblood pressure in patients with high blood pressure. Two hundred subjects wererandomly assigned to two groups. One group was instructed to exercise according tostrict schedule, and the other group was given medication to take. After 3 months,the researchers compared the change in blood pressure between the groups and foundthat the exercise groups experienced a greater drop in blood pressure on average.a. Is this an observational study or an experimental study?b. Explain why a blind study would be difficult to do in this situation.
The authors of a paper randomly selected two samples of patients admitted to the hospital after suffering a stroke. One sample was selected from patients who received biofeedback weight training for 8 weeks, and the other sample was selected from patients who did not receive this training. At the end of 8 weeks, the time it took (in seconds) to stand from a sitting position and then to sit down again (called sit-stand-sit time) was measured for the people in each sample. Data consistent with summary quantities given in the paper are given below. For purposes of this exercise, you can assume that the samples are representative of the population of stroke patients who receive the biofeedback training and the population of stroke patients who do not receive this training. Biofeedback Group 2.1 2.8 4.5 2.3 2.9 4.3 3.4 4.2 3.4 3.7 3.0 3.7 3.7 2.5 3.3 No Biofeedback Group 5.2 4.8 4.0 4.3 4.8 4.4 4.3 5.2 3.5 4.3 5.2 4.5 4.1 3.5 4.0 Conduct a test of hypothesis to test whether…
The authors of a paper randomly selected two samples of patients admitted to the hospital after suffering a stroke. One sample was selected from patients who received biofeedback weight training for 8 weeks, and the other sample was selected from patients who did not receive this training. At the end of 8 weeks, the time it took (in seconds) to stand from a sitting position and then to sit down again (called sit-stand-sit time) was measured for the people in each sample. Data consistent with summary quantities given in the paper are given below. For purposes of this exercise, you can assume that the samples are representative of the population of stroke patients who receive the biofeedback training and the population of stroke patients who do not receive this training. Biofeedback Group 2.2 2.9 4.6 2.4 3.0 4.4 3.5 4.3 3.5 3.8 3.1 3.8 3.8 2.6 3.4 No Biofeedback Group 5.2 4.8 4.0 4.3 4.8 4.4 4.3 5.2 3.5 4.3 5.2 4.5 4.1 3.5 4.0 Conduct a test of hypothesis to test whether…
Anna Fisher and colleagues (Fisher et al., 2014) predicted that kindergarten students should learn better in undecorated classrooms compared to decorated classrooms, because students should be less distracted in sparse classrooms without distractions such as posters, maps, children's artwork, etc. They had a group of 12 kindergarten age children participate in a science lesson in a classroom without decorations and a classroom with decorations. The students took a test on the material immediately after each lesson (scores range from 0 to 20). Below are the number of correct responses on both tests for each child. Do kindergarteners learn better in an undecorated compared to a decorated environment? Undecorated Decorated Subject (X1) (X2) 1 19 17 1. State the null and alternative 15 14 hypotheses using the appropriate 16 symbols. State whether the test is one- 15 or two-tailed 14 4 19 17 15 6. 2. State the degrees of freedom and 18 18 13 14 identify the critical value(s) at an alpha 8.…
To check the activation level of data scientists, a population of data scientists was asked to play games for a fixed time duration and their brain activation levels were tested. The outcome of this research stated that playing the mobile games for a fixed time duration improved the concentration level with an average brain activation level of 100 units. If a sample of 12 data scientists were tested for the same experiment, the brain activation levels were reported as follows: 105, 90, 91, 96, 96, 91, 100, 105, 99, 107, 103 and 92 a. Does this data suggest that the population mean reading for the brain activation level under the given conditions differs from 100? State and test the appropriate hypotheses using a significance level of 0.05. b. Find the 90% confidence interval, and check whether the above given sample lies within this interval or not?
For 6 months we worked with a group of 15 severely mentally handicapped individuals in an attempt to teach them self-care through imitation. For a second 6- month period, we used physically guided practice with the same individuals. For each 6-month session, we collected ratings on the level of required assistance (high 3Dbad) for each person. The data for each individual follows (on the next page). Was the assistance significantly reduced in the second 6-month period? (use alpha=D0.05) %3D
A certain prescription drug is known to produce undersirable side effects in 30% of all patients who use the drug. Among a random sample of 6 patients using the drug, find the proabability of no patient having the undersirable side effects.
Clothes dried outside smell better than those dried in a dryer because of a process called photolysis. Sunlight breaks down compounds that cause odor. A trained smeller is asked to smell a random sample of 20 towels. The smeller does not know it, but all of the 20 towels have been dried in the sun. The smeller is blindfolded and is not allowed to touch the towels but leans forward to smell the towel then rates the towel on a smell-scale of 1 to 10, where 1 is the an extremely unpleasant smell and 10 is a very good smell. A smell rating of 8 is typically attributed to a towel that is dried in the dryer. The mean smell rating for these 20 towels is approximately normal with a mean of 8.45 and the standard deviation is 0.887. A statistician performs a test of Ho: μ = 8 versus H₁ μ> 8 where is the true mean smell rating for all towels dried in the sun. This test yields a P-value of 0.0176. What conclusion would you make at the significance level a = 0.01? Because the P-value of 0.0176 > a…
Clothes dried outside smell better than those dried in a dryer because of a process called photolysis. Sunlight breaks down compounds that cause odor. A trained smeller is asked to smell a random sample of 20 towels. The smeller does not know it, but all of the 20 towels have been dried in the sun. The smeller is blindfolded and is not allowed to touch the towels but leans forward to smell the towel then rates the towel on a smell-scale of 1 to 10, where 1 is the an extremely unpleasant smell and 10 is a very good smell. A smell rating of 8 is typically attributed to a towel that is dried in the dryer. The mean smell rating for these 20 towels is approximately normal with a mean of 8.45 and the standard deviation is 0.887. A statistician performs a test of Ho μ = 8 versus H₁ μ> 8 where is the true mean smell rating for all towels dried in the sun. This test yields a P-value of 0.0176. What conclusion would you make at the significance level a = 0.05? Because the P-value of 0.0176 < α =…
A personal trainer wanted to test the effectiveness of two different workout routines. She took a random sample of 70 of her clients and, in a random order, had them complete one of the two routines for two weeks. Then, after a one-month waiting period, she asked them to come back and do the other routine for two weeks. After each two-week period of the exercise routines, she measured their performance on a physical fitness aptitude test. She found the average difference in aptitude scores between the two routines for each client was 30.4 with a standard error of 3.2. What would be her 85% confidence interval for the average difference in the effectiveness of the two routines? (3 decimal places) ( , )
This Exercise pertains to a 2015 study¹ which took a Swedish family that ate a conventional diet (non-organic), and then had them eat only organic for two weeks. Pesticide concentrations for several different pesticides were measured in µg/g creatinine by testing morning urine. Multiple measurements were taken for each person before the switch to organic foods, and then again after participants had been eating organic for at least one week. The results are pretty compelling, and are summarized in a short video³ which as of this writing has had over 30 million views online. The data are visualized in Figure 1 for eight different detected pesticides, and can be found in Organic Effect. How do pesticide levels in the body differ after eating organic versus non-organic? Concentration (mcg/g crt) Concentration (mcg/g crt) 0 5 10 15 24D Non-Organic Organic ETU Non-Organic Organic 1 Increase (a) Increase the sample size. (b) Simulate more bootstrap samples. Decrease Remain the same…
Compare the two separate scatterplots. In particular, how do the associtation compare between women with pets vs. women without pets? Does one group have more variation in systolic blood pressure than the other? If so, for which group? Does systolic blood pressure seem higher for common ages between the two groups? If so, for which group?

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