1. Catherine decided to compare the color distribution of M&Ms in randomly chosen bags of M&Ms to the theoretical distribution reported by M&M/ MARS consumer affairs. Below is the theoretical distribution reported on their website: Color Percentage Brown 30% Yellow 20% Red 20% Orange 10% Green 10% Blue 10% Catherine went to different stores and bought many large bags of M&Ms (treat this as a random sample of M&Ms). She dumped them into a large bowl and counted the number of each color. In total she observed a random sample of 509 M&Ms. The number observed of each color in her sample was: Color Frequency Brown 150 Yellow 114 Red 106 Orange 53 Green 43 Blue 43 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? Assume an alpha level of .01. (10 points) 2. The issue of how much the U.S. should spend to solve particular social problems is a complex matter, and people have diverse and conflicting ideas on these issues. The following table contains information from the 2006 GSS about race and attitudes on social welfare spending. Respondents were asked whether the U.S. is spending too much, too little, or the right amount of money to address welfare. Is this sufficient evidence that there a relationship between race and attitudes towards spending on social welfare? Use alpha=.05. (10 points) Respondent's Race White Black Hispanic Total Too little 128 41 21 190 Respondent's Attitudes Towards Spending on About right 97 32 21 250 Social Welfare Too much 185 31 19 235 Total 510 104 61 75 3. Below is the output for the regression of state teen birth rate in 1998 on percent of the total state population living in poverty in 1997. Use this information to answer parts a and b. Model Summaryb Adjusted R Std. Error of Model R R Square Square the Estimate 1 692 478 468 7.67905 a. Predictors: (Constant), Percent of total state pop. living in poverty 1997 b. Dependent Variable: Teen birth rate (births per 1,000 females ages 15-17), 1998Coefficients Standardized Unstandardized Coefficients Coefficients Model B Std. Error Beta Sig. Constant) 3.792 3.891 974 335 Percent of total state pop. 1.942 290 692 6.704 .000 iving in poverty 1997 a. Dependent Variable: Teen birth rate (births per 1,000 females ages 15-17), 1998 3 a. How much of the variability in teen birth rates in 1998 can be explained by the % of the total state population living in poverty in 1997? (1 points) b. What is the least squares regression line for the regression of state teen birth rate (1998) on percent of the total state population living in poverty (1997)? (2 points) 4. Based on the correlation matrix below, are there statistically significant correlations between outcome of job performance test, outcome of IQ test, and outcome of job motivation test? Include the correlation and the p- value for each significant correlation. (2 points) Correlations Outcome of job Outcome of IQ Outcome of job performance test test motivation test Outcome of job performance Pearson Correlation 474 635 test Sig. (2-tailed) 000 .000 N 60 60 60 Outcome of IQ test Pearson Correlation 474 047 Sig. (2-tailed) 000 .722 N 60 60 60 Outcome of job motivation Pearson Correlation 635 047 test Sig. (2-tailed) .000 722 N 60 60 60