Show that if a one-way analysis of variance is performed on the ranks of the observations instead of the observations themselves, it becomes equivalent to a test based on the H statistic.
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- A researcher is interested in whether North Americans are able to identify emotions correctly in people from other cultures. It is known that, using a particular method of measurement, the accuracy ratings of adult North Americans in general are normally distributed with a mean of 82 and a variance of 20. This distribution is based on ratings made of emotions expressed by other North Americans. In the present study, however, the researcher arranges to test 50 adult North Americans rating emotions of individuals from Vulcan. The mean accuracy for these 50 individuals was 78. What should the researcher conclude?Professor Hayashi wants to see if a new Canvas Homework system has an effect on how well students perform on Exam 2. The Exam 2 mean for all students who have ever taken his statistic course is 77.2. He collects data from a sample of 9 students who use the new Canvas Homework system. He finds the Exam 2 mean for this sample is 81.7 with a variance of 32.49. What is the effect size using Cohen's D.Researchers at UT Austin noticed that the seagrass beds in Corpus Cristi Bay (CCB) were taller and thicker than those in Lower Laguna Madre (LLM). They compared the sediment ammonium concentration, in the two locations. Following are the summary statistics on sediment ammonium concentration, in micromoles, obtained by the researchers. Equality of variances is not assumed. CCB: X₁ 115.1, s₁= 79.4, n₁ = 51 LLM: X₂ = 24.3, S₂ 10.5, n₂: 19 = a. At the 1% significance level, is there sufficient evidence to conclude that the mean sediment ammonium concentration in CCB exceeds that in LLM? b. Determine a 98% confidence interval for the difference μ1-µ2, between the mean sediment ammonium concentrations in CCB and LLM. Interpret your answer in (a) in words. c. Do the results in (a) and (b) provide the consistent results? Explain.
- A researcher believes that the mean earnings of top-paid actors, athletes and musicians are the same. The earnings (in millions of dollars) for several randomly selected people from each category are shown in the table below. It has been confirmed that the population variance for each group is equal and that earnings follow a normal distribution for top-pain actors, athletes and musicians. Use a 5% significance to test the claim. Job Actor Actor Actor Actor Actor Actor Actor Actor Actor Actor Actor Actor Actor Actor Athlete Athlete Athlete Athlete Athlete Athlete Athlete Athlete Athlete Athlete Musician Musician Musician Musician Musician Musician Musician Musician Musician Musician Musician Musician Musician Musician Musician Earnings 31 34 33 26 21 33 30 36 27 27 34 37 36 23 30 39 46 41 36 50 30 44 43 44 46 54 65 30 39 52 37 41 45 60 60 31 49 45 45 What is the factor variable? Top-Paid Job Type What is the response variable? Earnings Test Statistic: 15.2043 X P-Value: 0.0000✓ O…An analysis of variances produces dftotal = 35 and dfwithin = 28. For this analysis, what is dfbetween? Round your answer to the nearest whole number.A coin-operated coffee machine made by BIG Corporation was designed to discharge a mean of 7.3 ounces of coffee per cup. If it dispenses more than that on average, the corporation may lose money, and if it dispenses less, the customers may complain. Believing that the mean amount of coffee dispensed by the machine, u, is greater than 7.3 ounces, BIG plans to do a statistical test of the claim that the machine is working as designed. Technicians gather a random sample of fill amounts and find that the mean of the sample is 7.5 ounces and that the standard deviation is 0.6 ounces. Based on this information, answer the questions below. What are the null hypothesis (H,) and the alternative hypothesis (H,) that should be used for the test? H: u is ? H: u is ? In the context of this test, what is a Type I error? A Type I error is ? fact, u is ? v the hypothesis that u is ? v? v. when, in Suppose that BIG decides not to reject the null hypothesis. What sort of error might it be making? ?
- When performing follow-up tests after Analysis of Variance, the problem of multiple comparisons must be addressed in order to keep the familywise Type I Error rate at an acceptable level. In order to do so, tests many be corrected, protected, and/or selected. Briefly explain, using appropriate examples, what is meant by the terms corrected, protected, and selected.A one-way Analysis of Variance (ANOVA) was used to examine whether students’ scores on a standardized test is a function of the teaching method they received (either lecture only, hands-on learning only, or both together). The ANOVA was significant. Run post hoc tests (by hand!) to determine which pairs of the mean are significantly different. Do the math for each and then explain in what way are they different. Method N Mean SD Source df SS MS F Lecture Only 15 82.8 9.59 Between 2 736.53 368.27 5.34 Hands-On Only 15 88.53 8.73 Within 42 2895.47 68.94 Both 15 92.67 6.22 Total 44 3632 Total 45 88Students in one class are asked to complete the same questionnaire 3 times throughout the semester: at the beginning, at the midterm, and at the end. The purpose of the questionnaire is to track students' perception of their progress at different points in the semester. Scores at Time 1 (beginning of the semester), Time 2 (midterm), and Time 3 (end of semester) are compared against one another. What type of analysis of variance would be appropriate for examining the results from this dataset?
- please don't provide hand writtin solution....A large company that produces allergy medications claims that Americans lose an average of 40 hours of work to problems related to seasonal allergies. A consumer advocacy group believes that company's claim exhibits self-interest bias. In other words, the advocacy group believes that the actual mean number of missed hours is less than claimed. The advocacy group would like to obtain statistical evidence about this issue and takes a random sample of 100 American workers. They find that these 100 people lost and average of 38 hours due to seasonal allergy symptoms. The standard deviation is 9.5 hours. (c) Based on your selection from part (b), what is the value of the standardized test statistic for this significance test? (d) Based on your selection from part (b), what is the P-value for this significance test? (e) What is the correct decision for this test, using a 0.05 level of signifcance? A) Reject the null hypothesis B) Do not reject the null…A drug which is used for treating diabetes has potentially dangerous side effects if it is taken in doses which are larger than the required dosage for the treatment. A medical researcher believes that the variance in dosage is different for two tablets made by different production facilities. The sample variance of a sample of 11 dosages of tablet "A" is 0.013 . The sample variance of a sample of 28 dosages of tablet "B" is 0.01 . Construct the 90% confidence interval for the ratio of the population variances. Round your answers to four decimal places.