Exam 17: Nonparametric Statistics

The Kruskal-Wallis test is to be used to determine whether there is a significant difference in the satisfaction rating (alpha = 0.05)between three brands of boxed cake mix.Shoppers were asked to rate their satisfaction on various attributes and an aggregate satisfaction score ranging from 1-50 was computed.The following data were obtained: For this situation,the critical (table)chi-square value is _______.

A researcher wants to determine the efficacy of a training program directed at improving concentration,focus,and memory on college students.She selects a random sample of 16 individuals and have them take an assessment initial test before the training program,then the individuals complete the training program,and at the end they take a final test that's comparable to the initial test.The results are shown in the following table: The analyst uses a Wilcoxon matched-pairs signed rank test with a 0.05 significance level.The appropriate decision is ______.

The Wilcoxon test was used on 18 pairs of data.The total of the ranks (T)were computed to be 111 (for + ranks)and 60 (for - ranks).The z value for this test is ____.

A quality control supervisor wishes to determine whether the following measurements are random: For this purpose,the supervisor computes the median of the thirty observations above,and finds it is ______.Then she compares each measurement to the median and assigns an "L" to it if it is below the median and a "U" if it is above the median.She determines that the number of Ls and Us are ______ and ______,respectively.

A researcher wants to determine whether the means of two independent populations are the same.She has two independent random samples,one from each population,shown in the following table: She uses the Mann-Whitney U test and a significance level of 0.05.The test statistic is ______.

A researcher wants to determine whether the means of two independent populations are the same.She has two independent random samples,one from each population,shown in the following table: She uses the Mann-Whitney U test and a significance level of 0.05.Then σ_U is ______.

A researcher wants to determine the efficacy of a training program directed at improving concentration,focus,and memory on college students.She selects a random sample of 16 individuals and have them take an assessment initial test before the training program,then the individuals complete the training program,and at the end they take a final test that's comparable to the initial test.The results are shown in the following table: The analyst uses a Wilcoxon matched-pairs signed rank test with a 0.05 significance level.The observed z score is ______.

A researcher wants to study the effects of physical exercise on depression.She randomly selects a group of 24 individuals who are equally depressed.None of these individuals currently exercises.She then randomly assigns them in one of three groups: group 1 stays without exercising (sedentary group),group 2 exercises once a week,and group 3 exercises two times a week.Individuals in groups 2 and 3 meet with a personal trainer so they carry out a very similar exercising program,both in kinds of exercises and in intensity.After two months,the researcher has all individuals take a depression-assessment test.The score of the test goes from 0 = totally miserable to 100 = complete satisfaction. The scores are shown in the following table: The researcher uses a Kruskal-Wallis test and a significance level α = 0.05.The critical chi-square value is ______.

Charles Clayton monitors the daily performance of his investment portfolio by recording a "+" or a "-" sign to indicate whether the portfolio's value increased or decreased from the previous day. His record for the last eighteen business days is "- + + - - - + - - + + + - + + + + -". The number of runs in this sample is _________.

A researcher wants to study the effects of physical exercise on depression.She randomly selects a group of 24 individuals who are equally depressed.None of these individuals currently exercises.She then randomly assigns them in one of three groups: group 1 stays without exercising (sedentary group),group 2 exercises once a week,and group 3 exercises two times a week.Individuals in groups 2 and 3 meet with a personal trainer so they carry out a very similar exercise program (kinds of exercises and intensity).After two months,the researcher has all individuals take a depression-assessment test.The score of the test goes from 0 = totally miserable to 100 = complete satisfaction. The scores are shown in the following table: The researcher uses a Kruskal-Wallis test and a significance level α = 0.05.The sum of the ranks for group 3,T_3, is ______.

The Mann-Whitney U test is a generalization of the two sample t-test under the underlying assumptions of equality of variances.

A quality control supervisor wishes to determine whether the following measurements are random: For this purpose,the supervisor computes the median of the thirty observations above and compares each measurement to the median.She determines that the number of runs is ______.

Charles Clayton monitors the daily performance of his investment portfolio by recording a "+" or a "-" sign to indicate whether the portfolio's value increased or decreased from the previous day. His record for the last eighteen business days is "- + + - - - + - - + + + + + + + + -". The number of runs in this sample is _________.

Correlation coefficients may be computed for parametric and nonparametric data. If the data are interval data,which of the following should be used?

A disadvantage of nonparametric statistics is that the probability statements obtained from most nonparametric tests are not exact probabilities.

A production run of 500 items resulted in 29 defectives items.A defective item is coded as 1 and a good item as 0.The following is an output from Minitab. Runs Test: Defects Runs test for Defects Runs above and below K = 0.058 The observed number of runs = 57 The expected number of runs = 55.636 29 observations above K,471 below P-value = 0.574 Using α=0.1,the conclusion is __________________.

Many "Before and after" types of experiments should be analyzed using _______.

The appropriate test for comparing the means of two populations using ordinal-level data from two independent samples is the Mann-Whitney U test.

The appropriate test for comparing the medians of two populations using ordinal-level data from two related samples is the Wilcoxon test.

In the Wilcoxon test of the differences between two populations,the value z statistic was calculated to be 1.80.If the level of significance is 0.05,which of the following decisions is appropriate?