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# 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.

421
571
427
453
390
566
435
460
575
633 456
378
509
637
571
495
560
521
554
497 569
364
511
591
690
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.

Color Percentage
Brown
Yellow
Red
Orange
Green
Blue 30
20
20
10
10
10

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:

Color Frequency
Brown
Yellow
Red
Orange
Green
Blue 152
114
106
51
43
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? Use &#945; = 0.05.

See attached file for full problem description.