Exam 17: Nonparametric Statistics

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 to perform a runs test.She determines the number of runs and finds that the corresponding z score is ______.

The nonparametric alternative to linear regression is the Kruskal-Wallis test.

Statistical techniques based on fewer assumptions about the population and the parameters are called _______.

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?

The Mann-Whitney U test is implemented differently for small samples than for large samples.

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 sum of ranks for sample I 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 _______.

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 μ_U is ______.

Nonparametric statistical techniques are based on fewer assumptions about the population and the parameters compared to parametric statistical techniques.

In a Wilcoxon matched-pairs signed rank test with 20 matched-pairs of observations,the observed value of the ?T statistic based on sample data is 76.33.The corresponding observed z-value is ___________.

When only ordinal-level data are available,Spearman's rank correlation rather than the Pearson product-moment correlation coefficient must be used to analyze the association between two variables.

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

Spearman rank correlation values,r_x,range between +1 and 0.

Suppose a research uses the Mann-Whitney 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 U statistic is 29,n₁=8 and n₂ = 9 what is the the conclusion at α=0.05 is __________

The alternate hypothesis for a one-sample runs test 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 observed K statistic is ______.

The Wilcoxon test was used on 16 pairs of data.The total of the ranks (T)were computed to be 76 (for + ranks)and 60 (for - ranks).The z value for this test 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 value of μ_T 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.This is a ______ test,and the critical ______.

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 test,how many degrees of freedom should be used?