Exam 14: Analysis of Categorical Data

When doing a chi-square and goodness-of-fit test,the squared difference between the observed and theoretical frequencies should be large if a null hypothesis is to be rejected.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A brand manager is interested in determining if consumers prefer the new fragrance associated with a detergent.She surveyed 212 consumers and has them rank the new and old fragrances on a scale of 1 to 10.Of the 198 consumers who scored a different score on the new fragrance than on the old,the absolute values of the differences in their ratings were ranked.The smaller of the ranked sums,8,208,was for those individuals who rated the original fragrance higher. -Which nonparametric method is appropriate for analyzing these results?

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 -How many degrees of freedom are associated with this test?

The Wilcoxon rank sum test is similar to the Mann-Whitney U test.The results will be the same for both tests.

Which of the following should certainly be known to select a value in the chi-square distribution table?

If the parameters of the distribution of interest are not specified,it is impossible to perform a goodness-of-fit test.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Consider a multinomial experiment involving n = 200 employees of a large corporation.The personnel department recorded the number of employees who were absent during the weekdays. The null hypothesis to be tested is H₀ : P₁ = 0.10,P₂ = 0.25,P₃ = 0.30,P₄ = 0.20,P₅ = 0.15 -Test the hypothesis at the 5% level of significance with the following frequencies:

A chi-square test for independence is applied to a contingency table with 3 rows and 6 columns for two qualitative variables.The degrees of freedom for this test must be 10.

The Mann-Whitney U test and Wilcoxon rank sum test are equivalent to each other.

A random sample of n observations,each of which could be classified into exactly one of k categories,is selected.How many degrees of freedom does a goodness-of-fit-test with specified probabilities have?

The area to the right of a chi-square value is 0.025.For 5 degrees of freedom,the table value is:

For a random sample of 156 observations,the skewness of the data was calculated to be 0.112,while the kurtosis was calculated to be 3.96.Is there sufficient evidence to reject the null hypothesis of normality for this data at 0.05 significance level?

Which of the following refers to a nonparametric method to compare two populations,when the samples are independent and the data are either ordinal or interval,and where the normality requirement necessary to perform the parametric test is not satisfied?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A large department store records the number of returns per day in women's dresses for reasons such as wrong size;husband didn't like it,color,etc.The manager of the women's dresses department recalls from her statistics class in college that the Poisson distribution might describe such events.A random sample of 150 days is taken.The number of returns per day in the sample as well as the observed frequencies is shown in the table below: She tests the hypothesis that returns per day are Poisson distributed with a population mean equal to 1.90.Her significance level is 0.05 -Determine the calculated value of the chi-square test statistic.

A chi-square test of association in a contingency table with r rows and c columns has a chi-square distribution with rc-1 degrees of freedom.

The skewness is zero for all distributions,such as the normal,that are symmetric about their mean.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A business statistics professor indicates that students who receive higher than an 80 on the final exam will receive at least a B- in the course.The scores for a random sample of 24 students are listed below. -Which nonparametric method is appropriate for analyzing this set of test scores?

The coefficients of skewness and kurtosis,under the null hypothesis that the population distribution is normal,are:

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 appropriate table value for a test for independence at the 0.025 significance level?

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 -A matched pairs experiment yielded the following results: Number of positive differences = 20, Number of negative differences = 8 Number of zero differences = 2 Can we infer at the 5% significance level that the location of population 1 is to the right of the location of population 2?