Exam 14: Nonparametric Methods

The z-test approximation to the Wilcoxon signed rank test is used whenever the number of nonzero differences is at least ____________________.

In a Wilcoxon rank sum test n₁ = 12, n₂ = 15 and the sum of R₁ = 108. The value of the test statistic for the normal approximation is:

Diet programs A consumer research organization will evaluate the results of two diet programs,Take-It-Off and Melt-Away.Persons are randomly sampled from each of the programs and their weight loss results follow. Take-It- Off Melt-Away 150 130 75 68 40 20 68 54 30 27 98 -The test question is: Do the data indicate that the two programs are equally effective? State the null and alternative hypotheses. H₀: ____________________ H₁: ____________________

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 rank of the value in the third treatment and fourth block?

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 -The Wilcoxon signed rank test for paired samples is used to test the hypotheses $H _ { 0 } : m _ { d } = 0 \text { vs. } H _ { 1 } : m _ { d } \neq 0$ What is the calculated test statistic,W?

The ____________________ test is the nonparametric counterpart to the randomized block ANOVA design.

The chapter lists four major advantages to nonparametric testing.What are they?

The following statistics are drawn from two independent samples: R₁ = 800,n₁ = 25,R₂ = 1100 and n₂ = 28.Test at the 5% significance level to determine whether the two population medians differ.

Compared to a parametric test,Nonparametric tests use the information in the data more efficiently.

Nonparametric tests are useful when data are of the nominal or ordinal scale of measurement.

IRS As a guideline,a local Internal Revenue Service office recommends that auditors try to spend 16 minutes or less with taxpayers who are called for audit interviews.In a recent random sample of 22 interviews,the interview times were as shown below: 13 21 21 25 25 21 14 14 24 23 11 24 19 18 17 12 13 17 16 25 20 13 Using the appropriate statistical table,what is the most accurate statement we can make about the p-value test? p-value = ____________________

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? -On a multiple-choice exam consisting of ten questions with A through E as choices,the correct answers were: A A D A C B A D C B.Use these data to test the hypothesis that the answer sequence is random.What is the expected number of runs?

The nonparametric counterpart of the parametric one-way analysis of variance F-test is:

FAA The FAA recorded the number of complaints per month for three airlines.The data were: Airline Airline Airline 3248 2462 1544 2876 2838 2381 2943 3042 2279 3486 3211 2163 2777 1968 1459 -The test question is: Do the three airlines have the same median number of complaints? State the null and alternative hypotheses. H₀: _____________________________ H₁: _____________________________

The Kruskal-Wallis test requires that the scale of measurement of the data must be at least interval or ratio,and the samples are assumed to be randomly selected from their respective populations.

The significance level for a Wilcoxon signed rank test for one sample is 0.01.The alternative hypothesis is m ≠ m₀,and the sample size is 14.What is/are the appropriate critical value(s)? Separate your answers with commas,for example x,y,z,etc.

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 -Using the 0.025 level,do these data suggest that the median interview time for auditors from this office exceeds the recommend guideline? H₀: ____________________ H₁: ____________________ Test statistic = ____________________ Critical Value = ____________________ Conclusion: __________________________________ Interpretation: _______________________________________________________

The nonparametric counterpart to the randomized block design of the analysis of variance is:

Airline Ten business people who fly frequently were asked to rank four airlines in terms of the quality of service.The people assigned scores using a 5-point scale where: 1 = bad,2 = poor,3 = average,4 = good,and 5 = excellent.The results are shown below: Airline Person A B C D 1 1 3 5 2 2 5 4 2 1 3 2 5 3 2 4 4 2 4 1 5 3 3 1 5 6 4 4 5 3 7 3 4 1 4 8 2 5 2 1 9 5 3 4 2 10 5 5 4 3 -Which test is appropriate if you want to compare the quality of service of the four airlines?

Apartments Residents of two different high rise apartment units may or may not have the same consumer indebtedness.A sample from each results in the following outstanding debt amounts: East West 14340 12832 13160 5038 9746 10146 16042 10651 17566 15394 7986 -The test question is: Do residents of the two apartment units have similar debt medians? In testing the hypotheses,the significance level is 0.05.What are the appropriate critical values? Separate your answers with commas,for example x,y,z,etc.