Exam 14: Analysis of Categorical Data

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Students in a statistics course were given a written examination as well as a project to complete as part of their final grade.For a random sample of 10 students,the scores on both the exam and the project are given below. -Calculate the spearman rank correlation coefficient.

In a normal approximation to the Wilcoxon rank sum test,the standardized test statistic is calculated as z = 1.96.For a two-tail test,the p-value of the test is 0.025.

A chi-square goodness-of-fit-test is to be performed.If the degrees of freedom are 8,and α = 0.10,then the table chi-square value that defines the rejection region is:

When testing for independence in a contingency table with r rows and c columns,the degrees of freedom for the test statistic would be:

The significance level for a Wilcoxon signed rank test is 0.05.The alternative hypothesis is stated as: The location of population 1 is to the left of the location of population 2.The appropriate critical value for a sample of size 20 (that is the number of nonzero differences)is:

If the measure of skewness for a particular data set is positive then the data is skewed to the right.

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. -Consider the following contingency table.Is there sufficient evidence to reject the null hypothesis of no association between the two variables?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A study was conducted to determine whether the use of seat belts in vehicles depends on ethnic status in Detroit.A sample of 1,000 people treated for injuries sustained from vehicle accidents was obtained,and each person was classified according to (1)ethnic status (African American or non-African American)and (2)set belt usage (worn or not worn)during the accident.The data are shown in the table below. Ethnic Status -At 5% level of significance,what is the proper conclusion?

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. -Which nonparametric method is appropriate for analyzing these results?

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. -Do the data indicate that the median number of hours that working women spend each week on housework exceeds that of working men? Use two different methods to answer this question.

In the sign test for paired differences,the test statistic S has a:

Suppose that for a random sample of 14 observations of random variables X and Y we compute a Spearman's rank correlation of 0.52.Is there sufficient evidence to reject the null hypothesis of no relationship between X and Y?

A chi-square test for independence is applied to a contingency table with 4 rows and 4 columns for two qualitative variables.The degrees of freedom for this test must be 9.

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 following table provides the score on a performance evaluation of employees when first hired,and one year later. Employee Using the Wilcoxon signed rank test,is there evidence that the employees' evaluations improved over their first year?

In a normal approximation to the Wilcoxon signed rank test,the test statistic is calculated as z = 1.26.For a two-tail test,the p-value is:

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. -Can we infer at the 5% significance level that the population locations differ?

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. -Upon entering a business school,students are asked regarding their intended concentration.From past records the following proportions were determined,30% - management,15% - finance,20% - accounting,25% - marketing,and 10% - economics.For the newly admitted class of 350 students,the breakdown of preferences was as follows: 99 - management,66 - finance,59 - accounting,80 - marketing,and 46 - economics.Is there sufficient evidence that the newly admitted class is different from previous classes?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A large city is in the process of voting on a bond issue to build a covered sports arena.A local political analyst wishes to determine if the level of income will impact on the decision of the voters.He takes a sample of 350 who plan to vote in the upcoming election. Vote on Bond Issue -What is the calculated value of the test statistic?

The Wilcoxon signed rank test statistic is approximately normally distributed whenever the number n of nonzero differences in the sample is larger than:

In the sign test for paired differences,the test statistic S is the: