Stat 2000 International Exam Answers and Explanations, Exams of Data Analysis & Statistical Methods

The answers and explanations for the stat 2000 international exam. It includes questions on topics such as hypothesis testing, confidence intervals, and t-tests. Students can use this document to review and understand the concepts covered in the exam.

Typology: Exams

Pre 2010

Uploaded on 07/30/2009

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Stat 2000 International – Final - Answers
1. Correct answer: [1] Students who participated in the survey.
2. Correct answer: [4] The responses you receive should not be considered representative of all
shoppers in the chain because you spoke only with shoppers who were willing to participate in
the survey.
3. Correct answer: [2] cholesterol level
4. Correct answer: [4] The set of 40 answers you receive when you ask the students how many
hours they spend on the Internet per day.
5. Correct answer: [3] Both preceding statements are true.
6. Correct answer: [4] The outlier is a person who has about 8 brothers and weighs about 160
pounds.
7. Correct answer: [2] about 0.65
8. Correct answer: [3] about 0.1061
9. Correct answer: [4] 0.7
10. Correct answer: [3] 0.75
11. Correct answer: [2] about 0.0297
12. Correct answer: [3] For each sample size, the distribution is centered at about the same point,
which also is approximately the population mean. For n = 25, there is less variation among the
different sample means than when n = 9.
13. Correct answer: [3] $0.56
14. Correct answer: [2] about 0.5
15. Correct answer: [4] The manager can be 95% confident that the true average travel time
between customers is between 21.63 and 22.91 minutes.
16. Correct answer: [2] Ha: p < 1/2
17. Correct answer: [3] about 0.1538
18. Correct answer: [4] H0: Population mean = 400; Ha: Population mean < 400
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Stat 2000 International – Final - Answers

1. Correct answer: [1] Students who participated in the survey. 2. Correct answer: [4] The responses you receive should not be considered representative of all shoppers in the chain because you spoke only with shoppers who were willing to participate in the survey. 3. Correct answer: [2] cholesterol level 4. Correct answer: [4] The set of 40 answers you receive when you ask the students how many hours they spend on the Internet per day. 5. Correct answer: [3] Both preceding statements are true. 6. Correct answer: [4] The outlier is a person who has about 8 brothers and weighs about 160 pounds. 7. Correct answer: [2] about 0. 8. Correct answer: [3] about 0. 9. Correct answer: [4] 0. 10. Correct answer: [3] 0. 11. Correct answer: [2] about 0. 12. Correct answer: [3] For each sample size, the distribution is centered at about the same point, which also is approximately the population mean. For n = 25, there is less variation among the different sample means than when n = 9. 13. Correct answer: [3] $0. 14. Correct answer: [2] about 0. 15. Correct answer: [4] The manager can be 95% confident that the true average travel time between customers is between 21.63 and 22.91 minutes. 16. Correct answer: [2] Ha: p < 1/ 17. Correct answer: [3] about 0. 18. Correct answer: [4] H0: Population mean = 400; Ha: Population mean < 400

19. Correct answer: [2] Since the two confidence intervals overlap, we can be confident in concluding that the average stress level for females does not differ from the average stress levels for males. 20. Correct answer: [ANY] No correct answer provided - full credit for everyone. [Possible correct answers might be "If the population mean is really 23, the probability is 0.50 (and not 0.0003) that the mean of the 36 ages could be more than 23." or "If the population mean is really 23, the probability is 0.0003 that the mean of the 36 ages could be more than 25.16."] 21. Correct answer: [4] Sample No. 4 22. Correct answer: [1] A significance test of the null hypothesis that the means are equal. 23. Correct answer: [1] The p-value would increase. 24. Correct answer: [5] 10 pounds 25. Correct answer: [1] 2. 26. Answer: Randomly select and survey a sample of students from the list of all students who attend the school. 27. Answer: (a) Median weight about 250 pounds. (b) Heaviest person about 520 pounds. (c) About 25% above 330 pounds. 28. Answer: 4. None of the above 29. Answer: Test results are independent so we use: P(at least one of them positive) = 1 - (0.15) * (0.15) = 0. 30. Answer: You can start with the "Graphing Normal z-Score/Probability" calculator for example. Enter 64 for the mean and 2.6 for the standard deviation. Calculate the "Area left of" 62 (0.2209) and "Area right of" 70 (0.0105) and then subtract these two numbers from 1.0. This will tell us that the proportion of women between 62 and 70 inches tall is 1.0 - (0.2209 + 0.0105) = 0.7686. 31. Answer: You can start with the "Graphing Normal z-Score/Probability" calculator for example. Enter 64 for the mean and 2.6 for the standard deviation. Choose "Area left of" and type in the area (the red number) as 0.70. Then click on "Compute!" and the answer will be that 65.36 is the 70th^ percentile. 32. Answer: Assign the numbers 1 to 30 to the thirty students. In some way, randomly select 15 numbers between 1 and 30. The students with those numbers are assigned to the Web-based approach. The other students are assigned to the textbook approach.

44. Answer: There is a linear trend, with higher SAT scores associated with higher GPA scores. There seems to be no outlier. 45. Answer: The correlation is 0.70355475. This indicates that there is a quite strong positive association and also that the points are quite close to a line with positive slope. 46. Answer: GPA = -9.480994 + 0.011256661 * SAT

The p-value associated with SAT is <0.0001 (which obviously is < 0.05), i.e., the slope is significantly different from 0. Therefore, we can use the regression equation to predict GPA scores from SAT scores.

47. Answer: For 1000: around 1.7756671; for 1100: around 2.901333; for 1200: around 4.0269995.

The first and the last value (for SAT scores of 1000 and 1200) are least reliable. We are extremely extrapolating for the first value (a SAT score of 1000 is more than 40 below the smallest observed value - this person may not be admitted to the university at all). The predicted value for 1200 is above the maximum possible value of 4.00 for GPA scores and therefore also is not reliable.

48. Answer: The histogram is skewed towards the lower values. There are no outliers. The modal bar is the one from 3.0 to 4.0 (or, more precisely, from 3.001 to 4.001). 49. Answer: When assuming independence, this relates to a Bin(20,000, 650/2,300,000) distribution. The expected value is: n * p = 20,000 * (650/2,300,000) = 5.65. 50. Answer: No - this is not possible. As stated before, the maximum SAT score is 1600 while the maximum GPA score is 4.00. The regression equation already predicts a GPA score higher than 4.00 for a SAT score of 1200. Clearly, it is not possible to use this equation to predict GPA scores for all applicants to Utah State University, in particular not for applicants with SAT scores above 1200. Even for the range of SAT scores where data is available, i.e., from about 1040 to somewhat less than 1200, the linear regression equation may not be fully justified (correlation and regression are most relevant for scatter plots that show an elliptical point cloud - but the point cloud here has been cut off at 4.00 and therefore is not fully elliptical).