Exam 14: Analysis of Categorical Data

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:

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 -State the appropriate conclusion at the 0.05 significance level.

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 -State the appropriate null and alternative hypotheses for this test.

A chi-square test for independence with 10 degrees of freedom results in a test statistic of 17.894.Using the chi-square table,the most accurate statement that can be made about the p-value for this test is that 0.05 < p-value < 0.10.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A statistics professor is interested in seeing if his students performed better on the second exam than the first.For the 45 students who scored a different score on the second exam than the first,the absolute values of the differences in their scores were ranked.The smaller of the ranked sums,320,was for those individuals who scored lower on their second exam. -Is there evidence that the students did better on their second exam?

The cells in the contingency table reflect the responses to each combination of categories for the variables of interest.

For tests of independence,the expected frequencies depend only on the sample size.

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. -Is there sufficient evidence to reject the null hypothesis of no preference against a two-sided alternative?

What is the rationale for df = (r - 1)(c - 1)in conducting a chi-square test of independence for a contingency table with r rows and c columns?

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. -Calculate the appropriate test statistics.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A group of managers was asked whether they would be willing to adopt a pay-for-performance compensation package.Of the 18 respondents,12 indicated that they were willing to adopt a pay-for-performance compensation package,while 5 indicated that they would not. -Which nonparametric method is appropriate for analyzing these results?

We would typically use nonparametric tests only for ordinal data.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A recent survey asked 124 purchasing managers what they thought would happen to inflation over the next quarter.Of those managers who thought the inflation rate would change,73 thought inflation would be higher,while 40 thought it would be lower. -A production manager is interested in modeling the number of defects in a sheet of steel.After a production run of 260 sheets,the manager finds that the average number of defects per sheet is 1.2.In addition,he records the following frequencies: Is there evidence at the 5% level of significance that the distribution of defects does not follow the Poisson distribution?

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 -Why would anyone want to do a Goodness-of-Fit-test?

Skewness provides a measure of the weight in the tail,of a probability density function.

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 - What is the effect of decreasing the sample size?

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

To determine whether a single coin is fair,the coin was tossed 100 times,and the head was observed 60 times.The value of the test statistic is:

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A production manager was interested in the relationship between the amount of overtime incurred over a week and the total level of output for the week.The manager collected data over a 12-week period.The data are presented below: -The introduction of the blue M&M has not been received very well.Suppose the brand manager for M&M wants to drop a color and is trying to decide which color to drop.The manager asks a group of 120 life-long consumers of M&Ms which is their least favorite color.He tabulates his results as follows: Can you reject the null hypothesis that the consumers have no consensus on their least favorite color?

Comparing the output of strawberries grown on plots using fertilizer A with that grown on otherwise identical plots using fertilizer B,in order to make a general assessment of relative fertilizer effectiveness,may well call for a: