Exam 17: Nonparametric Statistics

A perfect Spearman correlation of +1 or −1 between two variables indicates

The one-sample runs test is a ______________________.

The null hypothesis in the Kruskal-Wallis test is _______.

A quality control supervisor wishes to determine whether the following measurements are random: 68.2 65 66.5 65 67.5 68 66 64.5 65.3 64.2 67.6 66.5 66.8 68.9 67 65 65 67 68 71 68.5 63.6 64.7 71.5 70.7 66 68.5 70.5 69.5 70.1 For this purpose, the supervisor computes the median of previous observations, and finds it is 67.9.Then she compares each measurement to that 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.

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

A local pediatrician office is interested in the 'no-show' appointment count for each of the 4 pediatricians.'No-show' appointments represent lost revenues because the physician is idle when patients do not show for their scheduled appointments.Using the data in the table below and an alpha of .10, what is the null hypothesis? Physician A Physician B Physiciaan C Physician D week 1 8 4 6 7 week 2 7 3 4 6 week 3 8 2 5 4 week 4 8 6 7 9 week 5 4 2 5 10

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: $\quad$ $\quad$ $\quad$ $\quad$ Sample I $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ Sample II 11.5 15.7 22.8 22.5 12.6 13.8 17.5 10.7 13.5 12.4 25.3 16.1 25.1 14.8 11.8 14.7 10.8 12.7 She uses the Mann-Whitney U test and a significance level of 0.05.The test statistic 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 has them take an initial assessment 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: Individ. Before After 1 79 81 2 74 73 3 81 82.5 4 75 82.5 5 72.5 85 6 75 90 7 67.5 83.5 8 57.5 72.5 9 62.5 87.5 10 77.5 80 11 61.5 92.5 12 57.5 80 13 61.5 71 14 72.5 84 15 64 78.5 16 71 97.5 The analyst uses a Wilcoxon matched-pairs signed rank test with a 0.05 significance level.The value of $\mu$ _T is ______.

Which of the following tests should be used to compare the means of three populations if the sample data is ordinal?

A table manufacturer makes tables at 12 different heights for different purposes.The CEO would like to know if customers in two different industries place the same value on each of the different heights based on a Likert scale.Ideally, the CEO would prefer that the preferences of the two industries be distinctly different from each other.Based on this, the CEO is hoping that the Spearman correlation coefficient works out to be a _____________.

The alternate hypothesis for a one-sample runs test is __________________.

A quality control supervisor wishes to determine whether the following measurements are random: 68.2 65 66.5 65 67.5 68 66 64.5 65.3 64.2 67.6 66.5 66.8 68.9 67 65 65 67 68 71 68.5 63.6 64.7 71.5 70.7 66 68.5 70.5 69.5 70.1 For this purpose, the supervisor uses a previous median of 67.9 and compares each measurement to the median to perform a runs test.She uses a significance level of 0.05.The appropriate decision is ______.

The Spearman correlation coefficient is calculated for a set of data on two variables, x and y.It appears that as the rank of x increases, the rank of y is decreasing.We would expect the Spearman correlation coefficient to be ________.

No assumptions on the distribution of the difference are needed for the use of the Wilcoxon matched-pairs signed rank.

What is the Spearman rank correlation coefficient for the following set of data? 19 21 25 22 33 30 24 28 31 35

A local pediatrician office is interested in the 'no-show' appointment count for each of the 4 pediatricians.'No-show' appointments represent lost revenues because the physician will be Idle when patients do not show for their scheduled appointments.Using the data in the table Below and an alpha of 0.10, what is the observed value of $\chi$ ²? Physician A Physiciaan B Physician C Physician D week 1 8 4 6 7 week 2 7 3 4 6 week 3 8 2 5 4 week 4 8 6 7 9 week 5 4 2 5 10

The Kruskal-Wallis test is an extension of the Mann-Whitney U test to 3 or more groups.

Suppose a research uses the Mann-Whitney U test to determine if there is a difference in the volume of text messages sent by a high school student living in a rural area versus an urban area during the month of December.Eight rural high school students and 9 urban high school students were included in the study.If, among all 17, the sum of the ranks W₂ produced from the urban high school is 88, the U₂ test statistic is _____________

A Kruskal-Wallis test is to be performed.There will be five categories, and alpha is chosen to be 0.01.The critical chi-square value is _______.

The HYPERLINK "http://www.statisticssolutions.com/mann-whitney-u-test" Mann-Whitney U test requires that the two samples under consideration have the same number of observations.