Exam 19: Nonparametric Statistics

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The sign test statistic has a(n)____________________ distribution.

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Song Ratings A music critic wanted to determine whether or not music listeners of different age groups evaluate a song differently.With this objective,he commissioned a survey that asked people their ratings of the most popular songs.The rating categories were: 1 = terrible,2 = fair,3 = good,and 4 = excellent.Each respondent was also asked to categorize his or her age as either: 1 = teenager,2 = young adult (20-34),3 = middle age (35-50),and 4 = over 50. The results are shown below. Song Ratings Teenager Young Adult Middle Age Senior 3 2 3 3 4 3 2 4 3 3 1 4 3 2 2 3 3 2 2 3 4 1 3 4 2 3 1 4 4 2 4 3 -{Song Ratings Narrative} What statement can be made about the p-value for this test?

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The Friedman test compares the locations of ____________________ populations where the data are generated from a randomized block experiment.

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Advertisement In a Kruskal-Wallis test to determine whether differences exist among three different advertisements,the following statistics were obtained: T1 = 884,n1 = 20,T2 = 756,n2 = 28,T3 = 1061,n3 = 25. -{Advertisement Narrative} Explain how to use the p-value for testing the hypotheses.

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The critical value is taken from the F-distribution whenever the test is a Kruskal-Wallis test.

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Customers' Ages The marketing manager of a Hot Dog Stand chain is in the process of examining some of the demographic characteristics of her customers.In particular,she would like to investigate the belief that the ages of the customers of hot dogs,fast-food hamburger,and fast-food chicken restaurants are different.To test this belief,the ages of eight randomly selected customers from each restaurant type were recorded and listed below.From previous analysis we know that the ages are not normally distributed. Customers' Agas Hot Dogs Hamburger Chicken 23 26 25 19 20 28 25 18 36 17 35 23 36 33 39 25 25 27 28 19 38 31 17 31 -{Customers' Ages Narrative} Explain how to use the p-value for testing the hypotheses?

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Frozen TV Dinner The general manager of a frozen TV dinner maker must decide which one of four new dinners to introduce to the market.He decides to perform an experiment to help make a decision.Each dinner is sampled by ten people who then rate the product on a 7-point scale,where 1 = poor,and 7 = excellent.The results are shown below. Tasts Ratings Respondent Dinner 1 Dinner 2 Dinner 3 Dinner 4 1 6 6 4 5 2 5 5 2 4 3 7 7 3 4 4 6 6 5 4 5 7 6 4 3 6 7 5 3 5 7 6 4 3 4 8 5 6 4 6 9 4 4 3 5 10 7 5 6 4 -{Frozen TV Dinner Narrative} Which statistical technique can the general manager use to help him make a decision?

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Customers' Ages The marketing manager of a Hot Dog Stand chain is in the process of examining some of the demographic characteristics of her customers.In particular,she would like to investigate the belief that the ages of the customers of hot dogs,fast-food hamburger,and fast-food chicken restaurants are different.To test this belief,the ages of eight randomly selected customers from each restaurant type were recorded and listed below.From previous analysis we know that the ages are not normally distributed. Customers' Agas Hot Dogs Hamburger Chicken 23 26 25 19 20 28 25 18 36 17 35 23 36 33 39 25 25 27 28 19 38 31 17 31 -{Customers' Ages Narrative} Does this data provide enough evidence at the 10% significance level to infer that there are differences in ages among the customers of the three restaurant types?

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Airlines Ranking Ten business people who fly frequently from Las Vegas to Miami were asked to rank four airlines in terms of the quality of service.The people assigned scores using a 5-point Likert 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 -{Airlines Ranking Narrative} Which test is appropriate if you want to compare the quality of service of the four airlines?

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The Kruskal-Wallis test can be used to determine whether a difference exists between two populations.However,to determine whether one population location is larger than another,we must apply the Wilcoxon rank sum test.

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H0 in the Wilcoxon rank sum test is that the two population ____________________ are the same.

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The alternative hypothesis for the Friedman test is that all the population locations differ.

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The Friedman test applies to which situation?

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Nonparametric methods are designed to test ordinal data.

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The Kruskal-Wallis test statistic can be approximated by a chi-squared distribution with k- 1 degrees of freedom (where k is the number of populations)whenever the sample sizes are all greater than or equal to:

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Song Ratings A music critic wanted to determine whether or not music listeners of different age groups evaluate a song differently.With this objective,he commissioned a survey that asked people their ratings of the most popular songs.The rating categories were: 1 = terrible,2 = fair,3 = good,and 4 = excellent.Each respondent was also asked to categorize his or her age as either: 1 = teenager,2 = young adult (20-34),3 = middle age (35-50),and 4 = over 50. The results are shown below. Song Ratings Teenager Young Adult Middle Age Senior 3 2 3 3 4 3 2 4 3 3 1 4 3 2 2 3 3 2 2 3 4 1 3 4 2 3 1 4 4 2 4 3 -{Song Ratings Narrative} Explain how to use the p-value for testing the hypotheses.

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In a Kruskal-Wallis test,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:

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When the sample size n is greater than 30,the Spearman rank correlation coefficient rs is approximately normally distributed with:

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A nonparametric method to compare two or more populations,when the samples are matched pairs and the data are either ordinal or interval but not normal,is the:

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Which of the following shows the calculation of the sample Spearman rank coefficient?

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