Exam 14: Analysis of Categorical Data

A chi-square goodness-of-fit-test is to be performed to see if data fit the Poisson distribution.There are 5 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 sample of 10 observations produces the following summary values: = 10815.472, = 72.48 and S² = 28.044 -What is the approximate value of kurtosis?

Traditionally,a professor likes to assign grades according to the following breakdown: 15% As,25% Bs,40% Cs,15% Ds,and 5% Fs.This year,she gave out 17 As,35 Bs,60 Cs,10 Ds,and 2 Fs.Is there any evidence that the professor has changed her grading scheme at 5% significance level?

A left-tailed area in the chi-square distribution equals 0.10.For 5 degrees of freedom the table value equals 9.236.

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 100 owners of CD recorders was taken.Each sample member was asked to assess the amounts of time in a month spent watching material he or she had recorded from television broadcasts and watching purchased or rented commercial CDs.The 100 differences in times spent were then calculated and their absolute values ranked.The smaller of the rank sums,for material recorded from television,was 2852.Discuss the implications of this sample result.

If the number n of non-zero sample observations is large,then the sign test is based on the normal approximation to the binomial with mean μ = 0.5n and variance σ² = 0.25n.

In 2008,the student body of a state university in Utah consisted of 30% freshmen,25% sophomores,27% juniors,and 18% seniors.A sample of 400 students taken from the 2009 student body showed that there are 138 freshmen,88 sophomores,94 juniors,and 80 seniors.Test with 5% significance level to determine whether the student body proportions have changed.

In a goodness-of-fit-test,suppose that the value of the test statistic is 13.08 and degrees of freedom = 6.At the 5% significance level,the null hypothesis 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. -Suppose that you have collected market survey data for gender and product purchase.Perform a chi-square test to determine if there is a different probability of purchase among men and women.Include in your answer the expected cell values under the null hypothesis. Gender

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 -Calculate the probability associated with each category and the expected frequencies.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Three choices of free gifts are offered to 270 persons who subscribed to a new magazine.The number of subscribers choosing each gift is shown in the table below.Assume the null hypothesis that the gifts are equally attractive to the subscribers.Use a 0.01 significance level. -State the null and alternative hypotheses.

Briefly discuss some advantages of nonparametric tests.

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. -What is the p-value of this test?

One of the benefits of the sign test for paired samples is that it provides a method to incorporate information about the magnitude of the differences between matched pairs.

In the sign test applications,the normal approximation to the binomial distribution may be used whenever the number of nonzero differences exceeds:

Consider a cell in a contingency table.Given the cell's row total of 200 and a sample size of 1,000,the cell's expected frequency:

A chi-square test for independence with 10 degrees of freedom results in a test statistic of 18.21.Using the chi-square table,the most accurate statement that can be made about the p-value for this test is that:

The Wilcoxon signed rank test provides a more accurate estimate of the p-value than the sign test for the same 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. -The manager of the return desk at a local department store records the dollar value of 25 randomly-selected returns.The data are presented below Is there sufficient evidence to reject the null hypothesis that the median return is $60 against a one-sided alternative that the median is above 60?

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. -When should you use a nonparametric test? If the normality assumptions are met,are you better off using a parametric t-test to a nonparametric Rank Test?