Exam 19: Nonparametric Statistics

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The Kruskal-Wallis test can be conducted as one or two-tail test.

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The normal approximation to the Wilcoxon signed rank sum test statistic is used whenever the sample size is large (more than 30).

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A financier whose specialty is investing in movie productions has observed that,in general,movies with "big-name" stars seem to generate more revenue than those movies whose stars are less well known.To examine his belief he records the gross revenue and the payment (in $ millions)given to the two highest-paid stars in the movie for ten recently released movies. A financier whose specialty is investing in movie productions has observed that,in general,movies with big-name stars seem to generate more revenue than those movies whose stars are less well known.To examine his belief he records the gross revenue and the payment (in $ millions)given to the two highest-paid stars in the movie for ten recently released movies.   Assume that the conditions for the conducting tests of hypotheses for ρ and β<sub>1</sub> (the two tests are identical)are not met.Do the data allow us to infer at the 5% significance level that payment to the two highest paid stars and gross revenue are linearly related? Assume that the conditions for the conducting tests of hypotheses for ρ and β1 (the two tests are identical)are not met.Do the data allow us to infer at the 5% significance level that payment to the two highest paid stars and gross revenue are linearly related?

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Movie Scripts ​ In general,before a producer agrees to make a movie,each script is thoroughly reviewed by movie editors.Suppose that the Big-Screen Film Company has recently received two scripts for new movies.To help them decide which one to produce,both are sent to 30 editors who rate the scripts to judge which one is better.Suppose that 10 editors rate script 1 better and 20 rate script 2 better. ​ ​ -{Movie Scripts Narrative} Explain how to use the p-value for testing the hypotheses at the 5% significance level.

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When the sample sizes from both populations are larger than ____________________,the Wilcoxon rank sum statistic has an approximate normal distribution.

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If Friedman test is applied to a data set that are generated from a randomized block experiment with 3 treatments and 5 blocks,then the rejection region at the 2.5% significance level is Fr > 12.8325.

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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  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 Narrative} What statement can be made about the p-value for this test? ​ ​ -{Song Ratings Narrative} What statement can be made about the p-value for this test?

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A two-sample t-test is the parametric counterpart of the Wilcoxon signed rank sum test for matched pairs.

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The null hypothesis for the Wilcoxon rank sum test is that the two populations are the same.

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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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The Kruskal-Wallis test is an extension of the Wilcoxon rank-sum test from two to more than two statistical populations.

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

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In a Friedman test for comparing four populations,provided that there as eight blocks,the test statistic is calculated as Fr = 10.98.If the test is conducted at the 5% significance level,the conclusion and p-value will be:

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The sign test is employed to compare two populations when the experimental design is matched pairs,and the data are ordinal but not normally distributed.

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The Wilcoxon signed rank sum test statistic is approximately normally distributed whenever the sample sizes are larger than:

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The Kruskal-Wallis test is a nonparametric alternative to:

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To apply the Wilcoxon rank sum test to determine whether the location of population 1 is different from the location of population 2,the samples must be:

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The data below are drawn from four independent populations: The data below are drawn from four independent populations:   Test at the 1% significance level to determine whether the population locations differ. Test at the 1% significance level to determine whether the population locations differ.

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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' 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' Ages Narrative} Using the appropriate statistical table,what statement can be made about the p-value for this test? ​ ​ -{Customers' Ages Narrative} Using the appropriate statistical table,what statement can be made about the p-value for this test?

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In a Friedman test for comparing three populations,provided that there are five blocks,the test statistic is calculated as Fr = 6.594.Then,the most accurate statement that can be made about the p-value is:

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