Exam 7: Chi-Square Tests for Categorical Variables

Use the following 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. -Test, at the 10% level, if there is a significant association between gender and smoking status among students at this university. Include all of the details of the test.

Use the following 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. Rows: Party Columns: Trust Media? Pearson Chi-Square = 15.320, DF = 2, P-Value = 0.000 -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 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. -6 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 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? Briefly explain.

Use the following 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 February 12, 2009 marked the 200^th 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. -Is it appropriate to use a chi-square test to test for an association between education level and belief about evolution? Briefly explain.

Use the following February 12, 2009 marked the 200^th 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 Are all colors equally likely for Milk Chocolate M&M's? Data collected from a bag of Milk Chocolate M&M's are provided. -Report the p-value for your test. What conclusion can be made about the color distribution for Milk Chocolate M&M's? Use a 5% significance level.

Use the following 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 In 2009, Gallup 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 Are all colors equally likely for Milk Chocolate M&M's? Data collected from a bag of Milk Chocolate M&M's are provided. -Which color contributes the most to the chi-square test statistic? For this color, is the observed count smaller or larger than the expected count?

Use the following In a survey conducted by the Gallup organization September 6-9, 2012, 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. -Is a chi-square test appropriate in this situation? Explain briefly.

Use the following In 2009, Gallup 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 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. -State the null and alternative hypotheses for testing if the color distribution for Milk Chocolate M&M's has changed since 2009.

Use the following 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? Explain briefly.

Use the following February 12, 2009 marked the 200^th 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 February 12, 2009 marked the 200^th 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 expected cell count for the (College Graduate, Do Not Believe) cell. Report your answer with one decimal place.

Use the following February 12, 2009 marked the 200^th 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.

In a 2012 survey, Gallup asked a random sample of U.S. adults if they would prefer to have a job outside the home, or if they would prefer to stay home to care for the family and home. Of the 504 males they surveyed, 391 said that they would prefer to have a job outside of the home. Of the 473 females they surveyed, 254 said that they would prefer a job outside of the home. Test, at the 5% level, if there is evidence of an association between sex and preference to have a job outside of the home. Include all details of the test.

Use the following 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?