Exam 14: Analysis of Categorical Data

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. -You want to get a gumball out of a gumball machine.You really like the ones colored blue.You can see that there are four different colors in the machine: blue,red,yellow,and white.You buy 40 gumballs and record the colors.Is there sufficient evidence to suggest that the distribution of colors is not uniform?

To compute the p-value of a matched pairs sign test,the binomial distribution is employed.

The number of degrees of freedom in a chi-square goodness-of-fit-test when population parameters are estimated is equal to the number of:

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 -What are the appropriate degrees of freedom?

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. -A campus administrator has found that 64% of all students view courses as very useful,20% as somewhat useful,and 16% as worthless.Of a random sample of 150 students taking business courses,105 found the course in question very useful,25 somewhat useful,and 20 worthless.Test at the 10% level the null hypothesis that the population distribution for business courses is the same as that for all courses.Carry out the calculations manually,and verify your answers using statistical software.

What characteristics of the data might lead us to use nonparametric tests?

If for a particular data set,the skewness = -0.2,and the kurtosis equals 2.1,then it can be inferred that:

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. -You are interested in determining whether there is an association between the age of an individual and the amount of their monthly long distance expenditures.You collect the following data from 12 individuals.What is the Spearman's rank correlation for this data?

The Wilcoxon signed rank test assumes that the population distribution in the difference of paired samples:

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. -A random sample of 10 students was asked to rate,in a blind taste test,the quality of two brands of wine one domestic and one imported.Ratings were based on a scale from 1 (poor)to 10 (excellent).The accompanying table gives the results.Use the Wilcoxon signed rank test at the 10% level of significance to test the null hypothesis that the distribution of the paired differences is centered on 0 against the alternative that the population of all student wine drinkers prefers the imported brand. Student

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. -Production records indicate that in the normal operation for a certain brand of computer hard drive,95% have no faults,3% have one fault,and 2% have more than one fault.For a random sample of 400 of these hard drives from a week's output,375 were found to have no faults,15 to have one fault,and 10 to have more than one fault.Test at the 5% level the null hypothesis that the quality of the output from this week conforms to the usual pattern.

In a normal approximation to the sign test,the standardized test statistic is calculated as z = 2.17.If the alternative hypothesis states that the location of population 1 is to the right of the location of population 2,then the p-value of the test is 0.015.

A goodness-of-fit-test is always conducted as a(n):

The Wilcoxon rank sum test provides a method to incorporate information about the magnitude of the differences between matched pairs.

For a chi-square goodness-of-fit-test,the calculated chi-square value is 7.21.If the table chi-square value is 10.645,what is the appropriate decision for this test?

The procedure for the Wilcoxon rank sum test requires that we rank each group separately rather than combining them together before assigning ranks.

The test statistic for the Jarque-Bera test for normality does not depend on the sample size.

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 -Calculate the value of the test statistic.

Nonparametric tests are preferred to parametric tests since they are always more powerful.

When the number n of nonzero differences in the sample is greater than 20,which of the following distributions provide a good approximation to the distribution of the Wilcoxon signed rank statistic?