Exam 14: Nonparametric Methods

Treatments Treatments Blocks 1 2 3 1 12 20 16 2 13 18 14 3 13 20 12 4 15 16 18 5 8 10 10 6 10 17 16 No assumptions are made about the population distributions or variances of the above sample data.The test question is: Are the medians of the treatments equal? -State the null and alternative hypotheses. H₀: _____________________________ H₁: _____________________________

Writers Eight professional food writers have been asked to rate the taste characteristics of a meat dish prepared first by flame grilling and then by charcoal grilling. After each of the dishes is prepared it is rated on a scale from 1 to 5 with 1 being best and 5 being worst. The results of the rating were: Writer Flame Charcoal A 5 1 4 4 B 4 2 2 2 C 1 2 -1 1 D 4 3 1 1 E 3 1 2 2 F 4 4 0 0 G 4 5 -1 1 H 2 3 -1 1 -In testing the hypotheses H₀: m_d = 0,H₁: m_d ≠ 0,data are drawn from a matched pairs experiment,and the following statistics are calculated: n = number of nonzero differences = 40; R+ = 238; R- = 582.Assume that the 5% level of significance is used.Calculate the z-approximation test statistic.

The significance level for a Wilcoxon signed rank test for one sample is 0.025.The alternative hypothesis is m > m₀,and the sample size is 14.What is the appropriate critical value?

A random sample of ten basketball players from the SLC revealed 3 (+ differences)who weighed more than 245 pounds.Test the null hypothesis that m_d = 0 versus the alternative hypothesis that m_d < 0.The p-value for the computed test statistic is:

Which of the following statements are not true?

In a Kruskal-Wallis test at the 5% significance level,there are four samples and the value of the test statistic is calculated as H = 8.79.The most accurate statement that can be made about the p-value is that it is:

Which of the following statements are not true?

For one sample,the Wilcoxon signed rank method tests whether the sample could have been drawn from a population having a hypothesized value as its ____________________.

Treatments Treatments Blocks 1 2 3 1 12 20 16 2 13 18 14 3 13 20 12 4 15 16 18 5 8 10 10 6 10 17 16 No assumptions are made about the population distributions or variances of the above sample data.The test question is: Are the medians of the treatments equal? -No assumptions are made about the population distributions or variances of the above sample data.The test question is: Are the medians of the treatments equal? What is the calculated value of the test statistic Fr?

An NHL executive says that players who incur penalty time during a game have a median time of 1.2 minutes in the penalty box. A random sample of 28 hockey players with penalty time produced 24 non-zero differences when a Wilcoxon signed rank test was used. The W (R+) equaled 156.5. The alternate hypothesis is m 1.2 minutes. Assume the population is symmetrically distributed. The computed test statistic in this instance equals:

Treatments Treatments Blocks 1 2 3 1 12 20 16 2 13 18 14 3 13 20 12 4 15 16 18 5 8 10 10 6 10 17 16 No assumptions are made about the population distributions or variances of the above sample data.The test question is: Are the medians of the treatments equal? -No assumptions are made about the population distributions or variances of the above sample data.The test question is: Are the medians of the treatments equal? What is the calculated value of the test statistic Fr?

John took a test that required him to rank order the importance of 15 items to help him survive in the desert.The following table shows his results along with the correct order. Item Inhn's Order Correct Order 1 1 4 2 11 9 3 5 3 4 12 15 5 6 12 6 10 5 7 3 1 8 15 10 9 8 14 10 9 7 11 14 11 12 4 2 13 13 13 14 2 6 15 7 8 Calculate and interpret the Spearman coefficient of rank correlation and use the 0.01 level of significance in testing whether its true value could be something other than 0.

Wilcoxon In a Wilcoxon signed rank test the following information describes the results: Number of nonzero differences = 12; R+ = 22; R- = 56.The hypothesis set is: H₀: m ≤ 33 H₁: m > 33 -Assume the population is symmetrically distributed.At a 0.05 significance level,what is the appropriate decision rule?

Dataset Consider the following data set: 11 11 12 13 15 16 16 17 18 19 20 22 22 22 22 25 -What is the rank assigned to the three observations of value 1.8?

The nonparametric counterpart to the paired sample,two-sample t-test is the:

What role does the binomial distribution play in the sign test,and when is it permissible to use the normal approximation in carrying out the test?

A nonparametric method to compare more than two populations,when the samples are independent and the data are either ranked or quantitative but not normal,is:

Treatments Treatments Blocks 1 2 3 1 12 20 16 2 13 18 14 3 13 20 12 4 15 16 18 5 8 10 10 6 10 17 16 No assumptions are made about the population distributions or variances of the above sample data.The test question is: Are the medians of the treatments equal? -No assumptions are made about the population distributions or variances of the above sample data.The test question is: Are the medians of the treatments equal? For the hypotheses,what is the appropriate critical value for the 0.025 significance level?

A randomized block design analysis of variance test corresponds to a:

The p-value for the computed test statistic is: