Exam 7: CHI-Square Tests for Categorical Variables

Use the following to answer the questions below: An insurance agent is interested in knowing if car crashes are more likely to occur on some days of the week than others. She selects a random sample of 250 insurance claims involving car crashes. Computer output from her chi-square test is provided. -The contribution for Friday is missing. Compute the contribution for Friday. Report your answer with three decimal places.

Use the following to answer the questions below: A political science professor at a small university wants to know if political party affiliation is significantly associated with trust in the media. He randomly selects 66 Democrats, 63 Republicans, and 41 Independents. Computer output of his chi-square analysis is provided. -The expected count for the (Independent, Yes) cell is missing. Compute the expected count for this cell. Report your answer with two decimal places.

Use the following to answer the questions below: The Gallup organization surveyed a random sample of American adults about their belief in the theory of evolution. The responses are summarized in the provided table. -Which opinion contributes the most to the chi-square test statistic? For that opinion, is the observed count larger or smaller than we would expect?

Use the following to answer the questions below: A political science professor at a small university wants to know if political party affiliation is significantly associated with trust in the media. He randomly selects 66 Democrats, 63 Republicans, and 41 Independents. Computer output of his chi-square analysis is provided. -Which cell has the largest contribution to the chi-square statistic? For this cell, is the observed count larger or smaller than the expected count?

Use the following to answer the questions below: Upon request, the Mars Company (the maker of M&M's) will provide the color distribution for their candies. As of August 2009, they noted that "Our color blends were selected by conducting consumer preference tests, which indicate the assortment of colors that pleased the greatest number of people and created the most attractive overall effect. On average, our mix of colors for M&M'S CHOCOLATE CANDIES is: M&M'S MILK CHOCOLATE: 24% cyan blue, 20% orange, 16% green, 14% bright yellow, 13% red, 13% brown." Data collected from a bag of Milk Chocolate M&M's are provided. We want to determine if this sample provides evidence that the color distribution has changed since August 2009. -Report the chi-square test statistic. Use three decimal places.

Use the following to answer the questions below: Upon request, the Mars Company (the maker of M&M's) will provide the color distribution for their candies. As of August 2009, they noted that "Our color blends were selected by conducting consumer preference tests, which indicate the assortment of colors that pleased the greatest number of people and created the most attractive overall effect. On average, our mix of colors for M&M'S CHOCOLATE CANDIES is: M&M'S MILK CHOCOLATE: 24% cyan blue, 20% orange, 16% green, 14% bright yellow, 13% red, 13% brown." Data collected from a bag of Milk Chocolate M&M's are provided. We want to determine if this sample provides evidence that the color distribution has changed since August 2009. -Report the p-value for your test. What conclusion can be made about the color distribution of Milk Chocolate M&M's? Use a 5% significance level.

Use the following to answer the questions below: Upon request, the Mars Company (the maker of M&M's) will provide the color distribution for their candies. As of August 2009, they noted that "Our color blends were selected by conducting consumer preference tests, which indicate the assortment of colors that pleased the greatest number of people and created the most attractive overall effect. On average, our mix of colors for M&M'S CHOCOLATE CANDIES is: M&M'S MILK CHOCOLATE: 24% cyan blue, 20% orange, 16% green, 14% bright yellow, 13% red, 13% brown." Data collected from a bag of Milk Chocolate M&M's are provided. We want to determine if this sample provides evidence that the color distribution has changed since August 2009. -Which color contributes the most to the chi-square test statistic? For that color, is the observed count larger or smaller than what we would expect under the null hypothesis?

Use the following to answer the questions below: February 12, 2009 marked the 200th anniversary of Charles Darwin's birth. To celebrate, Gallup, a national polling organization, surveyed 1,018 Americans about their education level and their beliefs about the theory of evolution. The survey results are displayed in the provided two-way table. Note that the expected counts for most cells appear in parentheses. -What are the degrees of freedom for the test?

Use the following to answer the questions below: February 12, 2009 marked the 200th anniversary of Charles Darwin's birth. To celebrate, Gallup, a national polling organization, surveyed 1,018 Americans about their education level and their beliefs about the theory of evolution. The survey results are displayed in the provided two-way table. Note that the expected counts for most cells appear in parentheses. -Using a 5% significance level and assuming the test statistic is = 127.451, compute the p-value and make an appropriate conclusion for this test. If there is a significant association between these two variables, describe how they are related.

Use the following to answer the questions below: The Gallup organization surveyed a random sample of American adults about their belief in the theory of evolution. The responses are summarized in the provided table. -Test, at the 5% level, if there is evidence that not all opinions are equally likely.

Use the following to answer the questions below: Are all colors equally likely for Milk Chocolate M&M's? Data collected from a bag of Milk Chocolate M&M's are provided. -If all colors are equally likely, how many candies of each color (in a bag of 420 candies) would we expect to see?

Use the following to answer the questions below: Upon request, the Mars Company (the maker of M&M's) will provide the color distribution for their candies. As of August 2009, they noted that "Our color blends were selected by conducting consumer preference tests, which indicate the assortment of colors that pleased the greatest number of people and created the most attractive overall effect. On average, our mix of colors for M&M'S CHOCOLATE CANDIES is: M&M'S MILK CHOCOLATE: 24% cyan blue, 20% orange, 16% green, 14% bright yellow, 13% red, 13% brown." Data collected from a bag of Milk Chocolate M&M's are provided. We want to determine if this sample provides evidence that the color distribution has changed since August 2009. -Is a chi-square test appropriate in this situation?

Use the following to answer the questions below: We have a random sample of 150 students (60 males and 90 females) that includes two variables: Smoke = "yes" or "no" and Gender = "female (F)" or "Male (M)." The two-way table below summarizes the results. -Is it appropriate to use a chi-square test to test for an association between gender and smoking status?

Use the following to answer the questions below: Are all colors equally likely for Milk Chocolate M&M's? Data collected from a bag of Milk Chocolate M&M's are provided. -State the null and alternative hypotheses for testing if the colors are not all equally likely for Milk Chocolate M&M's.

Use the following to answer the questions below: An insurance agent is interested in knowing if car crashes are more likely to occur on some days of the week than others. She selects a random sample of 250 insurance claims involving car crashes. Computer output from her chi-square test is provided. -Is a chi-square test appropriate in this situation?

Use the following to answer the questions below: February 12, 2009 marked the 200th anniversary of Charles Darwin's birth. To celebrate, Gallup, a national polling organization, surveyed 1,018 Americans about their education level and their beliefs about the theory of evolution. The survey results are displayed in the provided two-way table. Note that the expected counts for most cells appear in parentheses. -State the hypotheses for testing whether the data indicate that there is some association between education level and belief in evolution.

Use the following to answer the questions below: February 12, 2009 marked the 200th anniversary of Charles Darwin's birth. To celebrate, Gallup, a national polling organization, surveyed 1,018 Americans about their education level and their beliefs about the theory of evolution. The survey results are displayed in the provided two-way table. Note that the expected counts for most cells appear in parentheses. -Compute the contribution to the chi-square statistic for the (Postgraduate, Believe) cell. Report your answer to two decimal places.

Use the following to answer the questions below: Are all colors equally likely for Milk Chocolate M&M's? Data collected from a bag of Milk Chocolate M&M's are provided. -Calculate the chi-square test statistic. Report your answer with three decimal places.

Use the following to answer the questions below: In a survey conducted by the Gallup organization, 1,017 adults were asked "In general, how much trust and confidence do you have in the mass media - such as newspapers, TV, and radio - when it comes to reporting the news fully, accurately, and fairly?" The results are summarized in the provided table. We are interested in testing whether or not the four responses are equally likely. -Test, at the 5% level, if there is evidence that the four opinions are not all equally likely. Include all details of the test.

Use the following to answer the questions below: The Gallup organization recently conducted a survey of 1,015 randomly selected U.S. adults about "Black Friday" shopping. They asked the following question: "As you know, the Friday after Thanksgiving is one of the biggest shopping days of the year. Looking ahead, do you personally plan on shopping on the Friday after Thanksgiving, or not?" Their results, broken down by sex, are summarized in the provided two-way table. -Test, at the 1% level, if there is a significant association between sex and plans to shop the Friday after Thanksgiving. Include all details of your test.