Math 1530: Elements of Statistics
Exam I VERSION I
NAME:
INSTRUCTIONS: Take the class period to complete this exam. You may use a calculator, #2 pencils, 1/2 page of notes, and your brain. Do not share any materials and you must do your own work to receive any credit. Good luck!
1. The brand of soda is (a) quantitative continuous (b) quantitative discrete (c) categorical 2. The number of cars sold in a week is (a) quantitative continuous (b) quantitative discrete (c) categorical 3. The time until the tenth car is sold is (a) quantitative continuous (b) quantitative discrete (c) categorical 4. The number of coins in your pocket is (a) quantitative continuous (b) quantitative discrete (c) categorical 5. Outcomes of the (a) response; explanatory
variable depend on values of the (b) response; lurking
variable.
(c) lurking; response
(d) explanatory; response
Which of the following thirteen statements are true, and which are false? Mark (a) for true and (b) for false. 6. The standard deviation measures how far the data tend to be from 0. 7. Jack’s test score was at the 20th percentile and Jill’s was at the 75th percentile. This means about 55% of the scores fell between Jack’s and Jill’s scores. 8. A z-score tells the direction and number of means a data value is from the standard deviation. 9. The median lies to the right of the mean for a right-skewed distribution. 10. The regression line has the property that the sum of the squared errors (or sum of squared residuals) is as large as possible. 11. The first quartile divides a data set into a lower 75% and upper 25%. 12. About 99.7% of a population with a bell-shaped distribution lies within two standard deviations of the mean. 13. Approximately 25% of a population are above the third quartile. 14. Influential observations tend to lie far from most of the other data points in the x-direction, and they can have a large influence on the slope of the regression line. 15. The less spread out data are from their mean, the larger the standard deviation is. 16. Data with an r value of -0.98 are strongly correlated. 17. Two data sets with the same standard deviation should have the same mean. 18. If the correlation between two quantitative variables is 0.10, the variables have a strong linear relationship.
Use the following information to answer the next seven questions.
Squad n 1 20 2 43 3 17
Mean 22.45 18.23 19.00
StDev 5.88 7.03 6.96
Min. Q1 Median Q3 5.00 18.25 24.50 26.75 5.00 13.00 18.00 24.00 9.00 13.00 21.00 24.00
Max. 30.00 30.00 33.00
19. What would be the most appropriate description for the Squad 1’s distribution? (a) Left skewed
(b) Right skewed
(c) Symmetrical (d) Bell-shaped Curve
(e) Impossible to tell
20. Which squad had the lowest median number of zombies killed? (a) Squad 1
(b) Squad 2
(c) Squad 3
(d) 18
(e) 19
21. Based on the standard deviations, which squad had the largest spread? (a) 7.03
(b) 25
(c) Squad 1
(d) Squad 2
(e) Squad 3
22. What is the minimum value for Zombie Attack Squad 1? (a) 5
(b)16
(c) 18
(d) 25
(e) Impossible to tell.
23. Which of the following is true? (a) Squad 2 and Squad 3 have the same IQR, but Squad 2 has a lower median than Squad 3. (b) Squad 2 and Squad 3 have the same IQR, but Squad 2 has a higher median than Squad 3. (c) Zombie Attack Squad 2 and Zombie Attack Squad 3 have the same medians but different IQRs. (d) Zombie Attack Squad 2 has a smaller range than Zombie Attack Squad 3. (e) Zombie Attack Squad 1 has a smaller range than Zombie Attack Squad 2.
24. About what percent of Squad 2 killed more than 18 zombies? (a) 50%
(b) 25%
(c) 75%
(d) 100%
(e) 82%
25. The dot plot below represents one of the data sets displayed in the Zombie Attack boxplots above. Which squad do you think it represents? (a) 1
(b) 2
(c) 3
(d) 4
(e) Impossible to tell
The remaining questions on this page refer to the histogram below showing the hours worked per week for a sample of 39 statistics students for fall 2011.
26. How many students worked at least 10 hours but less than 20 hours? (a) 0
(b) 4
(c) 5
(d) 10
(e) 4/39
27. What shape best describes this distribution? (a) bell-shaped
(b) left-skewed
(c) right-skewed
(d) uniform
(e) bimodal
28. How many students worked at least 15 hours per week? (a) 5
(b) 7
(c) 11
(d) 17.9%
(e) 28.2%
29. What percent of the students worked less than 10 hours? (a) 8%
(b) 25.6%
(c) 28.2%
(d) 71.8%
(e) 95.45%
The following are Kelley Blue Book values for a Ford F-150 based on truck age in years. Age (years) Value ($)
1 2 3 4 5 16,905 15,450 11,700 11,380 9,935
We want to predict the value of a Ford F-150 based on its age. The following questions refer to the above data. 30. The equation of the regression line is given by which of the following? (a) yˆ = 9.74 − 0.0005x
(b) yˆ = 9.74x − 0.0005
(c) yˆ = −18, 477 + 1, 801x (e) yˆ = 18, 477 − 1, 801x
(d) yˆ = 1, 801 + 18, 477x
31. What is the value of the correlation coefficient r, correct to two decimal places? (a) 0.96
(b) -0.96
(c) 0.93
(d) -0.93
(e) 1
32. According to this regression model, what percent of the variation in the price of a used Ford F-150 truck is explained by the variation in its age? (a) 89%
(b) 93%
(c) 95.45%
(d) 96.36%
(e) 99.7%
33. Is the regression line a good model for this data set? (b) No. r is close to −1.
(a) No. The absolute value of the slope is not close to 1. (c) No. Very few of the data points lie near the regression line.
(e) Possibly, because r2 is close to 1.
(d) Possibly, because the slope is not close to 1.
34. Use the regression line model to predict the dollar of a 10 year old Ford F-150. (a) $18,477
(b) -$467
(c) $467
(d) $182,969
(e) $182,969
35. Would this regression line be useful for predicting the value of a 10 year-old F-150? (a) Yes, because regression lines are used to make predictions. (b) Yes, because r2 is moderately high. (c) No. This would be extrapolation, and the line predicts a really low value for a 10 year-old F-150. (d) No. Value really has nothing to do with the age. 36. Adding a new data point at (10 yrs, $9,000) would probably (a) be a good idea because some 10 year old F-150s are worth $9,000. (b) influence the other Blue Book values. (c) cause r2 to increase. (d) have an influence on the regression line equation.
(e) make children laugh.
37. A potential lurking variable might be (i) the condition of the F-150 (a) i
(b) ii
(ii) the number of miles driven per year (c) iii
(d) i and ii
(iii) the price of eggs (e) i, ii, and iii
38. If you had to identify exactly one of the data points as an outlier, which one would it be? (a) (1 yr, $16,905) (b) (2 yrs, $15,450) (c) (3 yrs, $11,700) (d) (4 yrs, $11,380) (e) (5 yrs, $9,935)
Christmas tree heights have a bell-shaped distribution with mean 65 inches and standard deviation 9 inches. A farmer samples 1000 trees. Use this to answer the next three questions. 39. One tree had a z-score of 3.25. Which is correct? (a) This tree height is 3.25 standard deviation below the mean (b) This tree height is 3.25 inches above the mean (c) This tree height can be considered as an outlier from the other tree heights (d) This tree height is about average (e) None of the above 40. Approximately what percentage of the tree heights fall between 56 and 74 inches? (a) 50%
(b) 68%
(c) 80%
(d) 95%
(e) 99%
41. Approximately how many trees have heights between 47 and 83 inches tall? (a) 680
(b) 990
(c) 950
(d) 500
42. Match the r values to the following scatterplots.
(a) (i) r = 0.05
(ii) r = −0.99
(iii) r = 0.84
(b) (i) r = 0.05
(ii) r = −0.99
(iii) r = −0.85
(c) (i) r = 0.84
(ii) r = −0.85
(iii) r = −.99
(d) (i) r = 0.84
(ii) r = −0.99
(iii) r = −0.85
(iv) r = 0.05
(iii) r = 0.84
(iv) r = 0.05
(e) (i) r = −0.85
(ii) r = −0.99
(iv) r = −0.85 (iv) r = 0.84 (iv) r = 0.05
(e) 36
Consider the data 6, 7, 10, 13. You must show your work. 43. What is the mean?
Answer: 44. What is the sample standard deviation? x
x−x
(x − x)2
6
7
10
13
Total: Answer:
The demand for snow cones each day for eight consecutive days was 15
18
23
25
21
47
25
28
Use this information to answer the following four questions. You must show your work. 45. What is the median? Answer: 46. What is the range? Answer: 47. What is the interquartile range?
Answer: 48. If exactly one data value is an outlier, which is it? Use the 1.5 × IQR rule. Answer:
