Exam 14: Analysis of Categorical Data

A chi-square test of a contingency table with 4 rows and 5 columns shows that the value of the test statistic is 22.18.The most accurate statement that can be made about the p-value for this test is that the p-value is:

The simplest nonparametric test to carry out is the Wilcoxon rank sum test.

If a sample of 12 observations is taken to perform a matched or paired sign test and there are 2 ties in the data,then the p-value is based on a binomial distribution with:

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A university is considering changing its mascot.In a survey of 150 students,it was found that 89 preferred the new mascot,44 preferred the old mascot,while the remaining had no opinion. -Admissions at a local university have traditionally had the following breakdown: 45% local students,30% from within state,15% from neighboring states,5% from elsewhere in the U.S.and the remaining 5% international students.In the current freshman class,there are 328 local students,255 in-state students,121 students from neighboring states,36 students from elsewhere in the U.S. ,and 25 international students.Assuming that all the seats of the freshman class were occupied,is there evidence that the admissions policy at the university is changing?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: In a recent survey,15 viewers were asked to rank their enjoyment of two television programs.Of those respondents who had a preference,4 preferred The Big Bang Theory while 8 preferred Criminal Minds. -Which nonparametric method is appropriate for analyzing these results?

A random sample of n observations,each of which could be classified into exactly one of k categories,is selected.Suppose that a null hypothesis specifies category probabilities that depend on the estimation of m unknown population parameters.How many degrees of freedom does a goodness-of-fit-test have when population parameters are estimated?

For a large sample,the Wilcoxon rank sum test can be approximated by the Student's t distribution with (n - 1)degrees of freedom.

Kurtosis is a statistic of a data set that describes the symmetry of the data.

In order not to violate the requirements necessary to use the chi-square distribution,each expected frequency in a goodness-of-fit-test must be:

A goodness-of-fit-test is to be performed to see if consumers prefer any of four package designs (A,B,C,andD)more than the other three.If a random sample of 60 consumers is selected,what is the expected frequency for category A?

In all the rank tests,normality is a required assumption for the underlying populations.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: In testing the hypotheses H₀ : The two population locations are the same H₁ : The two population locations are different,the following statistics were calculated: n = 40,T₊ = 245,and T_- = 575 with data drawn from a matched pairs experiment. -Why would anyone want to use a nonparametric test when there are so many powerful parametric tests?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: An airline is considering changing the color scheme of its planes' interiors.A focus group of 220 people was asked which color scheme they preferred.Of those who expressed a preference,87 preferred the new color scheme,while 121 preferred the old. -The introduction of the new blue M&M has been received very well.In fact,the brand manager for M&M wants to add a color and is trying to decide which color to add.The manager asks a group of 12 life-long consumers of M&Ms to rank these colors on a scale of 1 to 10.The data is presented below: Consumers of M&Ms Using the Wilcoxon signed rank test,is there evidence that consumers' rankings were higher for one color or the other? State any assumptions needed to answer this question.

A chi-square goodness-of-fit-test is to be performed to see if data fit the Poisson distribution.There are 8 categories,and the parameter λ must be estimated.How many degrees of freedom should be used?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A random sample of 12 working men was asked how many hours of housework they performed each week.Their responses were: A random sample of 10 working women was asked the same question.Their responses are listed below. -A random sample of 12 seniors in college was asked how many hours they spend on the Internet each week.Their responses were: A random sample of 10 juniors was asked the same question.Their responses are listed below. Use the Wilcoxon rank sum test to test against a two-sided alternative the null hypothesis that the central locations of the population distributions of number of hours spent on the internet are the same for college seniors and juniors.

The chi-square goodness-of-fit test is usually used as a test of multinomial parameters,but it can also be used to determine whether data were drawn from any distribution.

The Wilcoxon rank sum test is likely to generate the same results as the Mann-Whitney U test.

Whenever the expected frequency of a cell is less than 5,one remedy for this condition is to decrease the significance level.

The Mann-Whitney U test and the Wilcoxon rank test are only used for testing the medians for independent populations.

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