Exam 9: Inference for Categorical Data

Because statistical software plays such an important role in modern statistical applications,many studies have encouraged the use of technology in statistics courses.The Guidelines for the Assessment and Instruction in Statistics Education (GAISE)(Aliaga et al. ,2005)project was funded by the American Statistical Association to examine needs for college level statistics courses.One of the six recommendations from GAISE is the use of technology for developing conceptual understanding and analyzing data.A survey was sent to students at 100 different universities across the United States to access the relationship between ease of learning the statistical software program SAS and a student's currently level of SAS proficiency.The results of the survey are published in Jackson et al. ,2011,in the International Mathematical Forum journal and are shown below. Table 1.Two-way table for ease of learning SAS and SAS proficiency level. What is the column proportion,D,for students who find SAS difficult to learn and who are somewhat proficient in SAS?

The degree of freedom associated with a chi-square test for two-way tables with r rows and c columns is

The chi-square test for two-way tables can be used to test a _______.

Because statistical software plays such an important role in modern statistical applications,many studies have encouraged the use of technology in statistics courses.The Guidelines for the Assessment and Instruction in Statistics Education (GAISE)(Aliaga et al. ,2005)project was funded by the American Statistical Association to examine needs for college level statistics courses.One of the six recommendations from GAISE is the use of technology for developing conceptual understanding and analyzing data.A survey was sent to students at 100 different universities across the United States to access the relationship between ease of learning the statistical software program SAS and a student's currently level of SAS proficiency.The results of the survey are published in Jackson et al. ,2011,in the International Mathematical Forum journal and are shown below. Table 1.Two-way table for ease of learning SAS and SAS proficiency level. What is the value of K?

Large values obtained for the  ² two-way tables provide evidence _____ the null hypothesis.

Because statistical software plays such an important role in modern statistical applications,many studies have encouraged the use of technology in statistics courses.The Guidelines for the Assessment and Instruction in Statistics Education (GAISE)(Aliaga et al. ,2005)project was funded by the American Statistical Association to examine needs for college level statistics courses.One of the six recommendations from GAISE is the use of technology for developing conceptual understanding and analyzing data.A survey was sent to students at 100 different universities across the United States to access the relationship between ease of learning the statistical software program SAS and a student's currently level of SAS proficiency.The results of the survey are published in Jackson et al. ,2011,in the International Mathematical Forum journal and are shown below. Table 1.Two-way table for ease of learning SAS and SAS proficiency level. What is the value of J?

The expected counts should be exactly equal to the observed counts for a goodness-of-fit test?

An agency responsible for coordinating organ donations for the purpose of transplantation conducted a survey in four different regions of Canada.In each region-West,Prairies,Central,and Atlantic-separate surveys were conducted.One question addressed attitudes with respect to the use of unrelated living donors for kidney transplantation.The following table summarizes the findings in these regions. The agency was interested in determining if the proportion of people who approve of unrelated living kidney donation is the same across the various regions. Under the appropriate null hypothesis,the expected cell count for those who approve of unrelated living kidney donation in the Atlantic region and the contribution that cell makes to the value of the test statistic are,respectively,

A simple random sample of 100 college students was interviewed.They were asked what size pizza they usually ordered and what their favorite topping was.The results are presented below. Under the null hypothesis that there is no association between pizza size and pizza topping,what is the value of the expected count for a small pepperoni pizza?

Recent revenue shortfalls in a Midwestern state led to a reduction in the state budget for higher education.To offset the reduction,the largest state university proposed a 25% tuition increase.It was determined that such an increase was needed to simply compensate for the lost support from the state.Random samples of 50 freshmen,50 sophomores,50 juniors,and 50 seniors from the university were asked whether or not they were strongly opposed to the increase,given that it was the minimum increase necessary to maintain the university's budget at current levels.The results are given in the following table. Which hypotheses would be tested by a chi-square test based on these data?

When a police officer responds to a call for help in a case of spousal abuse,what should the officer do? A randomized controlled experiment in Charlotte,North Carolina,studied three police responses to spousal abuse: advise and possibly separate the couple,issue a citation to the offender,and arrest the offender.The effectiveness of the three responses was determined by re-arrest rates.The table below shows these rates. Suppose we wish to test the null hypothesis that the proportions of subsequent arrests are the same regardless of the treatment assigned.Which of the following statements is true?

Simple random samples of 350 women and 450 men from Michigan are obtained.The 800 people in the sample are categorized according to where they went to school: in state,out of state,or no college. The SPSS output for the above table is given below.The output includes the cell counts and the most expected cell counts.Expected counts are printed below observed counts. Under the null hypothesis that there is no association between college location and gender,what is the distribution of the chi-square statistic?

When a police officer responds to a call for help in a case of spousal abuse,what should the officer do? A randomized controlled experiment in Charlotte,North Carolina,studied three police responses to spousal abuse: advise and possibly separate the couple,issue a citation to the offender,and arrest the offender.The effectiveness of the three responses was determined by re-arrest rates.The table below shows these rates. What proportion of times were there no subsequent arrests out of all cases in which the assigned treatment was "Advise/separate"?

An insurance company has conducted a study of its accident claim experience and the size of the automobile involved in the accident.A random sample of its claim files over the past 12 months was selected and claims were categorized according to the size of car (compact,midsize,or large),and also according to the amount of damage (minor,extensive,or write-off).The following table summarizes the results for the sample of 360 claims. What would the appropriate null hypothesis be for this study?

Even though Puerto Rico is a commonwealth of the United States,there are many cultural differences between the states on the continent and the island of Puerto Rico.These differences include the way consumers handle problems with purchases.Two researchers surveyed owners of DVD players in the Northeast United States and in Puerto Rico.They asked those who had experienced problems with their DVD players whether they complained.The results are given in the table below. The SPSS output for the above table is given below.The output includes the cell counts,the expected cell counts,and the chi-square statistic.Expected counts are printed below observed counts. Chi-square = 0.855 + 3.744 + 0.276 + 1.204 = 6.079 What do we know about the P-value for testing the null hypothesis that the probability of complaining is the same for the United States and Puerto Rico?

Even though Puerto Rico is a commonwealth of the United States,there are many cultural differences between the states on the continent and the island of Puerto Rico.These differences include the way consumers handle problems with purchases.Two researchers surveyed owners of DVD players in the Northeast United States and in Puerto Rico.They asked those who had experienced problems with their DVD players whether they complained.The results are given in the table below. The SPSS output for the above table is given below.The output includes the cell counts,the expected cell counts,and the chi-square statistic.Expected counts are printed below observed counts. Chi-square = 0.855 + 3.744 + 0.276 + 1.204 = 6.079 Which cell contributes most to the chi-square statistic?

Because statistical software plays such an important role in modern statistical applications,many studies have encouraged the use of technology in statistics courses.The Guidelines for the Assessment and Instruction in Statistics Education (GAISE)(Aliaga et al. ,2005)project was funded by the American Statistical Association to examine needs for college level statistics courses.One of the six recommendations from GAISE is the use of technology for developing conceptual understanding and analyzing data.A survey was sent to students at 100 different universities across the United States to access the relationship between ease of learning the statistical software program SAS and a student's currently level of SAS proficiency.The results of the survey are published in Jackson et al. ,2011,in the International Mathematical Forum journal and are shown below. Table 1.Two-way table for ease of learning SAS and SAS proficiency level. Based on examining the graphical distribution of ease of learning SAS and SAS proficiency,do you think there is a relationship between these variables?

When computing the column portions for a two-way table,the sum of the column percentages should sum to _______.

An insurance company has conducted a study of its accident claim experience and the size of the automobile involved in the accident.A random sample of its claim files over the past 12 months was selected and claims were categorized according to the size of car (compact,midsize,or large),and also according to the amount of damage (minor,extensive,or write-off).The following table summarizes the results for the sample of 360 claims. Under the appropriate null hypothesis,the expected cell count for large cars that are a write-off and that cell's contribution to the value of the test statistic are,respectively,

Because statistical software plays such an important role in modern statistical applications,many studies have encouraged the use of technology in statistics courses.The Guidelines for the Assessment and Instruction in Statistics Education (GAISE)(Aliaga et al. ,2005)project was funded by the American Statistical Association to examine needs for college level statistics courses.One of the six recommendations from GAISE is the use of technology for developing conceptual understanding and analyzing data.A survey was sent to students at 100 different universities across the United States to access the relationship between ease of learning the statistical software program SAS and a student's currently level of SAS proficiency.The results of the survey are published in Jackson et al. ,2011,in the International Mathematical Forum journal and are shown below. Table 1.Two-way table for ease of learning SAS and SAS proficiency level. What is the first contribution to the ² statistic for the significance test to test for a relationship between ease of learning SAS and SAS proficiency based on the location of cell A?