# SAT Scores and M&M Statistics Questions

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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 α = 0.05.

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##### Solution Summary

This solution provides answers to a question about hypothesis testing.

###### Education

- BSc , Wuhan Univ. China
- MA, Shandong Univ.

###### Recent Feedback

- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
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