Exam 7: Chi-Square Tests for Categorical Variables

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. -How many degrees of freedom are there?

M&M's, the popular candy-coated chocolate treats, come in a variety of flavors. One of the newest varieties is Pretzel, and another popular variety is Peanut Butter. Does the Mars Company (the maker of M&M's) use the same color distribution (frequency of colors) for all varieties, or does it depend on variety? Data collected on the two varieties are displayed in the provided two-way table. Test, at the 5% level, if the samples provide evidence of an association between color and variety. Include all of the details of the test.

A 2009 study to investigate the dominant paw in cats was described in Animal Behaviour (Volume 78, Issue 2). The researchers used a random sample of 42 domestic cats. In this study, each cat was shown a treat (5 grams of tuna), and while the cat watched, the food was placed inside a jar. The opening of the jar was small enough that the cat could not stick its head inside to remove the treat. The researcher recorded the paw that was first used by the cat to try to retrieve the treat. This was repeated 100 times for each cat (over a span of several days). The paw used most often was deemed the dominant paw. The researchers want to determine if there is a significant association between sex of the cat and dominant paw. Computer output from the analysis is provided. Is it appropriate to perform the chi-test to test for an association between sex and dominant paw in cats? If so, perform the test. If not, briefly explain why. Rows: Sex Columns: Paw Pearson Chi-Square = 30.927, DF = 1, P-Value = 0.000

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. -How many degrees of freedom are there?

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. -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 Observed counts from a sample are provided in the following table. The expected counts from a null hypothesis are given in parentheses. -Based on the expected counts, which of the following is most likely the null hypothesis?

Use the following 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. -Test, at the 5% level, if there is evidence that car crashes are not equally like to occur on all days of the week. Include all details of the test.

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. -Test, at the 5% level, if there is evidence that the four opinions are not all equally likely. Include all details of the test.

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. The results are summarized below. Use the goodness-of-fit test to determine if there is evidence that the two choices are not equally likely. Use a 5% significance level.

Use the following to answer questions On November 15 - 18, 2012 Gallup 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. -Compute the expected cell counts for all cells. Report your counts to two decimal places.

Use the following to answer questions On November 15 - 18, 2012 Gallup 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.

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 -Test, at the 5% level, if there is a significant association between political party affiliation and trust in the media. Include all details of the test.

Use the following M&M's, the popular candy-coated chocolate treats, come in a variety of flavors. Two popular varieties are Milk Chocolate (sometimes referred to as "Plain") and Peanut. Does the Mars Company (the maker of M&M's) use the same color distribution (frequency of colors) for all varieties, or does it depend on variety? Data were collected on the two varieties and computer output for a chi-square test of association is provided. Rows: Variety Columns: Color Pearson Chi-Square = 6.183, DF = 5, P-Value = 0.289 -Is it appropriate to use a chi-square test to test for an association between variety and color? Briefly explain.

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. -Is a chi-square test appropriate for testing if all beliefs are not equally likely? Explain briefly.

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 -Is it appropriate to use a chi-square test to test for an association between political party and trust in the media? Explain briefly.

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 -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 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 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? 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. -What are the degrees of freedom for the test?

Are all colors equally likely for Dark Chocolate M&M's? Data collected from a bag of Dark Chocolate M&M's are provided. Test, at the 5% level, if this sample provides evidence that not all colors are equally likely for Dark Chocolate M&M's. Include all details of the test.