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Deceptive News. In the article "When News Reporters Deceive: The Production of Stereotypes" (Journalism & Mass Communication Quarterly, Vol. 84, No. 2, pp. 281-298), researchers D. Lasorsa and J. Dai investigated the relationship between authenticity and tone for news stories. Tone was measured by using a method of coding sentences and was categorized as positive, neutral, or negative. A sample of stories yielded the following data. At the 5% significance level, do the data provide sufficient evidence to conclude that an association exists between authenticity and tone?

Road Rage. The report Controlling Road Rage: A Literature Review and Pilot Study was prepared for the AAA Foundation for Traffic Safety by D. Rathbone and. Huckabee. The authors discussed the results of a literature review and pilot study on how to prevent aggressive driving and road rage. Road rage is defined as an incident in which an angry or impatient motorist or passenger intentionally injures or kills another motorist, passenger, or pedestrian, or attempts or threatens to injure or kill another motorist, passenger, or pedestrian." One aspect of the study was to investigate road rage as a function of the day of the week. The following table provides a frequency distribution for the days on which 69 road-rage incidents occurred.

At the significance level, do the data provide sufficient evidence to conclude that road-rage incidents are more likely to occur on some days than on others?

In each of Exercises $12.24-12.33$, apply the chi-square goodness-of-fit test, using either the critical-value approach or the$P-$value approach, to perform the required hypothesis test.
Observing that the proportion of blue M&Ms in his bowl of candy appeared to be less than that of the other colors, R. Fricker, Jr., decided to compare the color distribution in randomly chosen bags of M&Ms to the theoretical distribution reported by M&M/MARS consumer affairs. Fricker published his findings in "The Mysterious Case of the Blue M&Ms" (Chance, Vol. 9(4), pp. 19-22). The following table gives the theoretical distribution.
For his study, Fricker bought three bags of M&Ms from local stores and counted the number of each color. The average number of each color in the three bags was distributed as follows.

Do the data provide sufficient evidence to conclude that the color distribution of M&Ms differs from that reported by M&M/MARS consumer affairs? Use $\mathrm{Î\pm }=0.05$.

Consider the variables "gender" and "college".

Part (a): Group the bivariate data for these two variables into a contingency table.

Part (b): Determine the conditional distribution of gender within each college and the marginal distribution of gender.

Part (c): Determine the conditional distribution of college within each college and the marginal distribution of college.

Part (d): Does an association exist between the variables "gender" and "college" for this population? Explain your answer.

A chi-square independence test is to be conducted to decide whether an association exists between two variables of a population. One variable has six possible values, and the other variable has four. What is the degrees of freedom for the ${\mathrm{χ}}^2$statistic?

In given exercise use either the critical-value approach or the P-value approach to perform a chi square independence lest. provided the conditions for using the test are met.

Siskel In the classic TV show Sneak Previews, originally hosted by the late Gene Siskel and Roger Ebert, the two Chicago movie critics reviewed the weeks new movie releases and

then rated them thumbs up (positive), mixed, thumbs down (negative). These two critics often saw the merits of a movie differently. In general, however, were ratings given by Siskel and Ebert

associated? The answer to this question was the focus of the paper "Evaluating Agreement and Disagreement Among Movie Reviewers" by A. Agresti and L. Winner that appeared in Chance

(Vol- 10(2), pp-10-14). The following contingency table summarizes ratings by Siskel and Ebert for 160 movies.

At the 1% significance level, do the data provide sufficient evidence to conclude that an association exists between ratings of Siskel and Ebert?

In given exercise use either the critical-value approach or the P-value approach to perform a chi square independence lest. provided the conditions for using the test are met.

Diabetes in Native Americans. Preventable chronic diseases are increasing rapidly in Native American populations, particularly diabetes. F. Gilliland et al. examined the diabetes issue in the paper "Preventative Health Care among Rural American Indians in New Mexico" (Preventative Medicine, Vol. 28, pp. 194-202). Following is a contingency table showing cross-classification of educational attainment and diabetic state for a sample of 1273 Native Americans (HS is high school).

At the 1% significance level, do the data provide sufficient evidence to conclude that an association exists between education level and diabetic state for native Americans?