SAT Scores and M&M Statistics Questions
1. As reported by the College Entrance Examination Board in National College-Bound Senior, the mean verbal score on the Scholastic Assessment Test (SAT) in 1998 was 505 points out of a possible 800. A random sample of 25 verbal scores for last year yielded the following data.
At the 10% significance level, does it appear that last year's mean for verbal SAT scores is greater than the 1998 mean of 505 points? Note: = 513.4, s = 85.5. (Hint: Since the population standard deviation is not given, use the t-test using the critical value approach.)
2. Observing that the proportion of blue M&Ms in his bowl of candy appeared to be less than that of the other colors, Ronald D. 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 article "The Mysterious Case of the Blue M&Ms" (Chance, 1996, Vol. 9(4), pp. 19-22). The following is 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 α = 0.05.
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