Practice exam # 1 .ps



Practice Exam (1) STAT202, Safi

Fall 2003

Section 1: Multiple-Choice

Questions 1 through 3 refer to the following information:

Some people think that drinking wine (in moderation) offers some protection against heart attacks. Data are given on wine consumption and death rate from heart attacks in 19 developed Western countries. Here is a stem-and-leaf of the wine consumption data:

0 | 7888

1 | 23689

2 | 45799

3 | 9

4 |

5 | 8

6 | 5

7 | 9

8 |

9 | 1

1. The distribution of the wine consumption is

a) Symmetric.

b) Right skewed.

c) Left skewed.

d) Uniform.

2. Because of the shape of the distribution, we know that the mean is

a) Larger than the median.

b) About the same as the median.

c) Nonsense, because the data have a nominal scale.

d) Smaller than the median.

3. Here is a scatter diagram of heart disease death rate versus wine consumption, the scatter diagram shows that

a) Countries that drink more wine have higher death rates from heart disease.

b) The amount of wine a country drinks is not related to its heart disease death rate.

c) Countries that drink more wine have lower death rates from heart disease.

d) None of the above.

4. A professor records the values of several variables for each student in her class. These include the variables listed below. Which of these variables is categorical?

a) Score on the final exam (out of 200 points).

b) Final grade for the course (A, B, C, D, or F).

c) The total number of points earned in the class (i.e., the total of the points on all exams and quizzes in the course. The maximum number of points possible is 500).

d) The number of lectures the student missed.

5. A financial analyst's sample of six companies' book value were

$25 $7 $22 $33 $18 $15

The sample mean and sample standard deviation are (approximately):

a) 20 and 79.2 respectively

b) 20 and 8.9 respectively.

c) 20 and 8.12 respectively.

d) 120 and 8.9 respectively.

6. Consider the following box plots of the grades in a course in statistics for each sex where the "+" shows the mean of the distribution.

[pic]

Which of the following is correct?

1. About 50% of the male students have grades between 50 and 70.

2. The female students have higher mean and median.

3. The mean is greater than the median for males and females.

4. The male students have less variability than the female students.

7. A researcher observes that, on average, the number of divorces in cities with Major League Baseball teams is larger than in cities without Major League Baseball teams. The most plausible explanation for this observed association is

a) the presence of a Major League Baseball team causes the number of divorces to rise (perhaps husbands are spending too much time at the ballpark).

b) the high number of divorces is responsible for the presence of a Major League Baseball teams (more single men means potentially more fans at the ballpark, making it attractive for an owner to relocate to such cities).

c) the association is due to common response (major league teams tend to be in large cities with more people, hence a greater number of divorces).

d) the observed association is purely coincidental. It is implausible to believe the observed association could be anything other than accidental.

8. There is an approximate linear relationship between the height of females and their age (from 5 to 18 years) described by:

Height = 50.3 + 6.01(age)

where height is measured in cm and age in years. Which of the following is not correct?

a) The estimated slope is 6.01 which implies that children increase by about 6 cm for each year they grow older.

b) The estimated height of a child who is 10 years old is about 110 cm.

c) The estimated intercept is 50.3 cm which implies that children reach this height when they are 50.3/6.01=8.4 years old.

d) The average height of children when they are 5 years old is about 50% of the average height when they are 18 years old.

9. A research study has reported that there is a correlation of r=-0.59 between the eye color (brown, green, blue) of an experimental animal and the amount of nicotine that is fatal to the animal when consumed. This indicates:

a) Nicotine is less harmful to one eye color than the others.

b) The lethal dose of nicotine goes down as the eye color of the animal changes.

c) The researchers need to do further study to explain the causes of this negative correlation.

d) The researchers need to take a course in statistics because correlation is not an appropriate measure of association in this situation.

10. The scatterplot below plots, for each of the fifty states, the infant mortality rate (deaths per 1000) X in 1990 in the state versus the percent of 18-year-olds in the state Y in 1990 that graduated from high school.

[pic]

The correlation between X and Y is r = -0.54. If instead of plotting these variables for each of the fifty states, we plotted the values of these variables for each county in the United States, we would expect the value of the correlation r to be

a) much higher and probably near 1 since there are many more counties than states.

b) + 0.54 (the magnitude is the same, but the sign should change).

c) smaller.

d) exactly the same.

11. A scientist obtained measurements on salinity ([pic]) and water flow ([pic]) in Pamlico Sound, North Carolina. The summary statistics were:

|[pic] |[pic] |[pic] |[pic] |[pic] |

|23.9 |9.1 |2.1 |3.00 |-0.63 |

The slope of the equation of the least squares regression line of [pic] on [pic]is

a) 0.9

b) -0.9

c) -0.441

d) 0.24

12. A lurking variable is

a) the true variable that is explained by the explanatory variable.

b) any variable that produces a large residual.

c) a variable that is not among the variables studied but that affects the response variable.

d) the true cause of a response.

Questions 13-15 refer to the following information:

Assume that scores on a math aptitude test follow a normal distribution with a mean 70 and standard deviation 8.

13. The minimum and the maximum scores of the middle 68% of students are:

a) 62 and 78

b) 54 and 86

c) 46 and 94

d) 65 and 75

14. The probability that a randomly selected student scores higher than 58 is

a) 0.0668

b) 0.4332

c) 0.9332

d) 1.0000

15. The best 33% of students are eligible for an advanced math program. How high have students to score in order to be eligible?

a) 0.44

b) 73.52

c) 66.48

d) 70.33

16. The monthly earnings of computer programmers are normally distributed with a mean of $4,000. If only 1.7% of programmers have monthly incomes of less than $2,834, what is the value of the standard deviation of the monthly earnings of the computer programmers?

a) 2.12

b) 550

c) 1222

d) 1336

The residuals plot shows

a) No violations of regression assumptions.

b) The existence of an influential point.

c) The straight line is not a good model.

d) Errors do not have constant variance.

17. The following is a scatterplot of the calories and sodium content of several brands of meat hot dogs. The least squares regression line has been drawn in on the plot.

[pic]

Based on the least-squares regression line in the scatterplot, one would predict that a hot dog containing 100 calories would have a sodium content of about

a) 600

a) 400

b) 350

c) 70

18. If removing an observation from a data set would have a marked change on the position of the least-squares regression line fit to the data, the point is called

a) a response.

a) a residual.

b) influential.

c) explanatory.

19. A study of class attendance and grades among first-year students at a state university showed that in general students who attended a higher percent of their classes earned higher grades. Class attendance explained 16% of the variation in grade index among the students. The correlation coefficient between percent of classes attended and grade index is

a) 0.16

b) 0.256

c) 0.40

d) -0.40

Section Two: Free-Response Problems

1. The following data elements represent the amount of time (rounded to the nearest second) that 15 randomly selected customers spent in line before being served at a branch of First County Bank.

183 121 140 198 199

90 62 135 60 175

350 110 185 85 172

a) Find the five-number summary.

b) Construct a labeled boxplot for this data. Show all your work.

c) Describe the distribution of the amount of time.

2. The average grades of 8 students in statistics and the number of absences they had during the semester are shown below.

| |Number of Absences |Average Grade |

|Student |(x) |(y) |

|1 |1 |94 |

|2 |2 |78 |

|3 |2 |70 |

|4 |1 |88 |

|5 |3 |68 |

|6 |4 |40 |

|7 |8 |30 |

|8 |3 |60 |

a) Find the correlation coefficient between the average grade and number of absences.

b) Find the equation of the regression line for predicting the average grade from number of absences.

c) Explain carefully in terms of the average grade from number of absences the meaning of the intercept and the slope in the regression line in part (b).

d) What percent of the variation in the average grade can be explained by number of absences? What does this tell you about the goodness of the model?

e) If a student missed 8 classes, what is the predicted grade? What is the corresponding residual?

a) The correlation coefficient between the average grade and number of absences is

r = - 0.915

b) The equation of the regression line for predicting the average grade from number of absences is Y= 92.83 - 8.94 X

c) The intercept: if the student attended all the classes (did not miss any class) then his/her expected grade is about 93.

The slope: for every extra absence the expected grade of the student will drop by about 9 points.

d) The value of r2 is 0.837. This means that about 84% of the variability in the average grades of the students is due to the number of their absences during the semester. This is a high percentage indicating that the model is good and valid for prediction.

e) The predicted value is [pic] and the residual is e=30-21.31=8.69.

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[pic]

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