Exam 14: Nonparametric Methods

Apply the Kruskal-Wallis test to determine if there is enough evidence at the 5% significance level to infer that at least one of the population medians differs from the others. Sample 23 25 25 22 27 22 25 17 19 20 19 21 18 20 26 H₀: ______________________________________ H₁: ______________________________________ Test statistic = ____________________ Critical Value = ____________________ Conclusion: ________________________________ Interpretation: _________________________________________________________

A Wilcoxon rank sum test for comparing two independent samples involves two sample sizes: 8 and 6.The alternate hypothesis is m₁ ≠ m₂.Use a 0.10 significance level.What are the appropriate table values? Separate your answers with commas,for example x,y,z,etc.

In a Wilcoxon signed rank test for matched pairs with n = 35,the rank sums of the positive and negative differences are 380 and 225,respectively.The value of the standardized test statistic (that is,the value of z approximation test statistic)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 -The test question is: Can we conclude at the 5% significance level that there are differences in service quality among the four airlines? Using the appropriate statistical table,what statement can be made about the p-value for the above test?

In general,when should a nonparametric technique be used instead of its parameter counterpart?

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 test statistic?

Seven Dwarfs Several years ago a television station interviewed individuals and asked them to name the "Seven Dwarfs" from the story of "Snow White." The amount of time (in seconds)to name the dwarfs was recorded by age group.The data were: Under 12 12 to 25 Over 25 60 120 75 45 65 45 38 60 75 30 48 55 35 150 100 -The test question is: Do the different age groups require the same median time to name the Dwarfs? In testing the hypotheses,what is the appropriate critical value for the 0.05 significance level?

The value of the test statistic in a Kolmogorov-Smirnov test for normality is D = 0.199,and it is based on a sample of 20 observations.What conclusion can you draw at the 5% significance level? Hypotheses: _______________________ Test statistic = ____________________ Critical Value(s)= ____________________ Conclusion: ___________________________

Seven Dwarfs Several years ago a television station interviewed individuals and asked them to name the "Seven Dwarfs" from the story of "Snow White." The amount of time (in seconds)to name the dwarfs was recorded by age group.The data were: Under 12 12 to 25 Over 25 60 120 75 45 65 45 38 60 75 30 48 55 35 150 100 -The test question is: Do the different age groups require the same median time to name the Dwarfs? What is the calculated test statistic H?

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? What is the rank of 1544 from Airline C?

The ____________________ test for normality can be used for samples of any size,including those that are too small.

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? In testing the hypotheses,the significance level is 0.10.What are the appropriate critical values? 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 -The Wilcoxon signed rank test for paired samples is used to test the hypotheses $H _ { 0 } : m _ { d } = 0 \text { vs. } H _ { 1 } : m _ { d } \neq 0$ At the 0.05 significance level,what are the critical values? Separate your answers with commas,for example x,y,z,etc.

In a Wilcoxon signed rank test for matched pairs,the test statistic is calculated as W = 48.The alternative hypothesis is H₁: m_d > 0.If there are n = 10 nonzero differences,and the 5% significance level is used,then the:

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? State the appropriate conclusion employing a 0.05 significance level.

An NBA executive says that players who substitute as the sixth, seventh and eighth positions for the games starting five players have a median playing time of 24 minutes. A random sample of 25 substitutes (6, 7 or 8) produces 20 non-zero differences in a Wilcoxon signed rank test and a W (R+) equal to 146. The alternate hypothesis is m 24 minutes. Assume the population is symmetrically distributed. The computed test statistic in this situation equals:

Nonzero Number of nonzero differences = 14; R+ = 16; R- = 89. The hypothesis set is: H₀: m ≥ 22,H₁: m < 22 -Assume the population is symmetrically distributed.At a 0.05 significance level,state the appropriate decision rule.

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? What is the rank for 12832 debt amount?

A husband and wife ranked 8 houses that they visited that were for sale.The rankings are shown in the following table. Hause Husband Wife 1 3 1 2 6 3 4 2 4 1 3 5 6 6 7 4 7 2 5 5 7 Calculate and interpret the Spearman coefficient of rank correlation and use the 0.05 level of significance in testing whether its true value could be something other than 0.

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 appropriate conclusion employing a 0.05 significance level.