Exam 18: Nonparametric Methods

For eight randomly selected states,the following table lists the per capita beer consumption (in gallons)and the per capita wine consumption (in gallons). Beer Wine 32.2 3.1 29.4 4.4 35.3 2.3 34.9 1.7 29.9 1.4 28.7 1.2 26.8 1.2 41.4 3.0 Calculate the rank correlation coefficient when beer consumption = x,and wine consumption = y.

A random sample of 11 third-year medical school students took a comprehensive written exam as well as a comprehensive oral exam.The scores on both exams are given below.It is established that both test scores have highly nonnormal distributions. Student Written exam score Oral exam score 1 60 55 2 72 78 3 33 60 4 89 87 5 61 79 6 65 82 7 25 41 8 80 58 9 92 95 10 48 64 11 65 70 The medical examination board wants to know if the oral exam scores are higher than the written exam scores.State the appropriate null hypothesis for this problem.

A study was conducted to investigate the effect of an intervention protocol on IQ tests.Nine randomly selected students were tested. Before After 100 106 111 112 93 95 92 90 99 107 85 100 117 126 110 105 98 110 Calculate T^- and T⁺

The __________________ test is a nonparametric counterpart of a one-way ANOVA F test.

The Kruskal-Wallis test is the nonparametric counterpart of the:

An international economist believes that there is a significant relationship between the amount of debt and the rate of unemployment.He randomly selected six countries to determine if there is a significant relationship between debt and unemployment rate.In the following table,debt figures for the 6 countries are given in billions of dollars and the corresponding unemployment rate is given in percentages.He also discovered that both the distribution of debt and the distribution of unemployment rate were highly skewed.Use Spearman's rank correlation and determine if there is a significant correlation between debt and unemployment rate.Show the rank correlation. Unemployment Country Debt Rate 1 1 5 2 3 5 3 5 8 4 1 4 5 6 8 6 6 12

The EPA has stipulated that the Pollution Standard Index (PSI)for clean air standards is to average no more than 100.A random sample of 9 days for the city of Acorn showed PSI readings of 144,85,90,120,150,105,93,130,and 115.Assume the population of PSI readings is highly nonnormal.The EPA wants to determine if there is significant evidence to conclude that Acorn's air is dirtier than the stipulated clean air standards.Which one of the following tests is appropriate for this problem?

In order to perform the ________________ test,all of the observations in p samples are combined into a single set and all of the values in the single set are ranked from smallest to largest.After ranking,the sum of the ranks for each of the p samples is calculated.

Two coffee-vending machines are studied to determine whether they distribute the same amounts.Samples are taken and the number of ounces is recorded for each machine. Machine A Machine B 6.10 5.99 5.95 6.01 5.98 5.98 6.01 5.96 6.00 6.08 5.95 5.89 6.02 6.01 6.04 6.00 5.99 5.97 6.06 6.00 What is the test statistic T?

For eight randomly selected states,the following table lists the per capita beer consumption (in gallons)and the per capita wine consumption (in gallons). Beer Wine 32.2 3.1 29.4 4.4 35.3 2.3 34.9 1.7 29.9 1.4 28.7 1.2 26.8 1.2 41.4 3.0 Test H₀: p_s = 0 vs.H_A: p_s > 0 for the relationship between beer consumption and wine consumption at the state level at ? = .05.

A sign test is a test of hypothesis about the population mean.

The EPA has stipulated that the Pollution Standard Index (PSI)for clean air standards is to average no more than 100.A random sample of 9 days for the city of Acorn showed PSI readings of 144,85,90,120,150,105,93,130,and 115.The EPA wants to test to determine if Acorn's air is dirtier than the stipulated clean air standards.Assume the population of PSI readings is highly nonnormal and state the null hypothesis.

Which one of the following nonparametric methods can be used to determine the strength of the relationship between two variables?

Which one of the following nonparametric methods can be considered as an extension of the Wilcoxon rank sum test?

Refer to the MegaStat/Excel output for the Wilcoxon signed ranks test given in the table below. At a significance level of .01,which one of the following rejection point conditions is correct regarding the null hypothesis H₀: D₁ and D₂ are identical probability distributions and the alternative hypothesis of H_a: D₁ is shifted to the left of D₂.

The ______________ test is a nonparametric method that requires data consisting of matched pairs.

A student is trying to decide if it is cheaper to order blank CDs over the Internet or to buy them at local electronics stores.Listed below are the prices (in dollars)quoted for boxes of 200 blank CDs from various manufacturers. \ Internet Local Electronics Stores 26.00 33.98 27.99 37.75 31.50 38.99 32.75 35.79 27.00 33.99 27.98 34.79 24.75 29.98 28.15 33.00 29.99 32.00 29.99 On the average,can we conclude that Internet purchases are significantly less than electronics store purchases? Test at ? = .05

Five years ago,the average starting salary of a new college graduate with a major in marketing was $34,000.A random sample of 10 graduates from this year's graduating class of a local university yielded the following starting salaries in thousands of dollars: 28,36,25,37,35,24,38,45,39,36.The local university wants to determine if the median starting salary for marketing graduates has increased in the last five years. State the alternative hypothesis.Assume that the population of starting salaries in marketing is not normally distributed.

The Wilcoxon rank sum test requires that two independent samples being compared must have equal sample sizes.

In order to perform the ________________ test,all of the observations in two samples are combined into a single set and all of the values in the single set are ranked from smallest to largest.