Answer the following questions

Researchers want to determine whether all bags of M&M's have the same proportion of colors regardless of the flavor of M&M's. To test this, they sampled randomly king-size bags of each flavor and recorded their findings in the table. Flavor M&M's Color Red Orange Yellow Green Blue Brown Original 24 11 29 17 9 14 Peanut 15 20 30 25 15 19 Almond 22 17 21 12 28 7 Part A: What are the correct degrees of freedom for this table? (2 points) Part B: Calculate the expected count for the number of green peanut M&M's. Show your work. (3 points) Part C: Is there sufficient evidence that there is a difference in the proportion of colors for the different flavors of M&M's? Provide a statistical justification for your conclusion. (5 points) A group of random students is surveyed about which part-time jobs the students have held, if any. The results are given in the table. Number of Part-time Jobs Babysitter Waiter Sales Clerk Cashier No Job 163 55 72 141 169 To analyze this information, which inference procedure is appropriate to use? O Chi-square goodness-of-fit test O Chi-square test of homogeneity O Chi-square test of independence O Two-proportion z-test O Two-proportion t-testWhat is the value of x for the two-way table? A B C X 46 21 15 Y 25 32 29 Z 37 23 28 0.0074 O 11.7342 O 12.256 O 13.4683 O 13.944Which of the statements are correct? I. A condition for using the chi-square goodness-of-fit test is that all expected counts must be at least five. II. The chi-square goodness-of-t test uses 1 n degrees of freedom. III. A condition for using the chi-square goodness-of-fit test is the observations are based on a random sample. 0 | only 0 ll only 0 l and Ill only 0 II and Ill only A chi-square test for homogeneity is conducted on three populations and one categorical variable that has three values. Computation of the chi-square statistic yields x2 = 2.05. What is the p-value? O p > 0.25 O 0.05