Practice Mid-Term Exam

1. Practice Mid-Term Exam Question 1.Classify the following random variable as to whether it is discrete or continuous. The number of people served at a McDonalds on a certain day. • Discrete • Continuous

2. Question 2.A frequency distribution based on six classes gave the following relative frequencies for the first five classes: 0.06, 0.10, 0.18, 0.26, 0.24. What is the relative frequency for the remaining class? • 0.05 • 0.10 • 0.16 • 0.20

3. Question 3.In order to rate TV shows, phone surveys are sometimes used. Such a survey might record several variables. Which of the following variables is qualitative? • The number of persons watching the show. • The ages of all persons watching the show. • The number of times the show has been watched in the last month. • The name of the show being watched.

4. Question 4.When the sample mean is larger than the sample median, the distribution of the sample is • Approximately symmetric • Skewed right • Skewed left • Heavy tailed

5. Question 5.Consider the following two samples: Sample 1: 3 4 2 1 2 3 5 Sample 2: 3 9 1 7 1 2 9 Which sample has the largest standard deviation? • Sample 1 • Sample 2 • The standard deviations will be equal • Can’t tell from the data

6. Question 6.The time required to assemble a bicycle has a mean of 42 minutes and a standard deviation of 5 minutes. The distribution of assembly times is mound shaped. What percent of assembly times are between 37 and 47 minutes? • approximately 68% • approximately 81.5% • approximately 89% • approximately 95%

7. Question 7.The scores of the top ten finishers in a women’s golf tournament are listed below. 71 67 67 72 76 72 73 68 72 72 Find the median score. • 67 • 72 • 71 • 74

8. Question 8.Given the following five number summary, find the interquartile range (IQR). 29 37 50 66 94 • 29 • 50 • 65 • 32.5

9. Question 9.Given the following least squares prediction equation. = – 173 + 74x, we estimate y to ________ by _________ with each 1-unit increase in x. • increase, 74 • decrease, 74 • decrease, 173 • increase, 173

10. Question 10.In statistics, what is a sample? • A set of data that characterizes some phenomenon. • A set of data selected from a population. • The number of measurements on a particular subset of the population. • A number that represents an estimate for a population parameter. • An inference about a population.

11. Question 11.If all the measurements in a large data set are approximately the same magnitude except for a few measurements that are very much smaller than the other measurements, how would the mean and median of the data set compare to each other and what shape would the histogram of the data set have? (a) The mean would be larger than the median and the histogram would be skewed to the left. (b) The mean would be smaller than the median and the histogram would be skewed to the left. (c) The mean would be equal to the median and the histogram would be symmetrical. (d) The mean would be smaller than the median and the histogram would be skewed to the right. (e) The mean would be larger than the median and the histogram would be skewed to the right.

12. Question 12.The correlation between two variables, x and y, is .956. State the coefficient of determination and explain just what this coefficient "determines".

13. Question 13.In a bell‑shaped distribution, what is the approximate percent of the measurements have a z‑score between ‑2 and 2?

14. Question 14.The boxplots below are of female and male exercise per week in hours. Compare and contrast the results of the two samples. Be sure to tell all that the boxplots reveal about the two groups of students. ‑‑‑‑‑‑‑‑ Female ‑‑‑I + I‑‑‑‑ ** * O O ‑‑‑‑‑‑‑‑ ‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑ Male ‑‑‑‑‑I + I‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑ ‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑ ‑‑‑‑‑‑‑‑+‑‑‑‑‑‑‑‑‑+‑‑‑‑‑‑‑‑‑+‑‑‑‑‑‑‑‑‑+‑‑‑‑‑‑‑‑‑+‑‑‑‑‑‑‑‑ 4.0 8.0 12.0 16.0 20.0

15. Question 15.The least-squares regression line of y on x is The line which makes the coefficient of determination as small as possible. The line that minimizes the square of the vertical distance between observed values of y and those predicted by the line, ŷ. The line which best splits the data in half, with half of the points above the line and half below the line. The line which best predicts the value of x for a given value of y. The line that connects all the points None of the above.

16. Question 16. In which scatter diagram is r = 0.9811? a) b) c) d) e)

17. Question 17. For a scatter diagram of (x, y) pairs, the coefficient of determination is 80%. This means: • 80% of the data points are in the confidence interval. • We are 80% confident that the least squares-regression line is correct. • The correlation coefficient is 0.64. • There is a strong positive correlation between x and y. • 80% of the total variation in the response variable is explained by the least squares regression line.

18. Question 18.A faculty group wants to determine whether job rating (x) is a useful linear predictor of raise (y). Using the method of least squares, the faculty group obtained the following prediction equation: ŷ = $14,000 – $2,000x. The estimated slope of the line is for a 1-point increase in an administrator’s rating, we estimate the administrator’s raise to decrease $2,000. TRUE FALSE

19. Question 19.The number of absences (x) and the final grade (y) of 9 randomly selected statistics students yielded the following least-squares regression equation: ŷ = -2.75x + 96.14 • Determine the predicted final grade of a student who had 6 absences. • Determine the residual of a data point for which x = 8 and y = 76.

20. Question 20.An engineer wants to use the weight of a car to predict the gas mileage. The following fitted line plot gives the least-squares regression line based on the weight (in hundreds of pounds) and miles per gallon for 15 domestic cars.

22. Which of the following could be the equation of the least-squares regression line depicted by the fitted line plot? (need hats on Miles per gallon) • Miles per gallon = 44.3 - 0.7*weight (in hundreds of pounds) • Miles per gallon = 44.3 + 0.7* weight (in hundreds of pounds) • Miles per gallon = 27.1 - 1.2* weight (in hundreds of pounds) • Miles per gallon = 27.1 + 1.2* weight (in hundreds of pounds) • None of a), b), c), or d) is correct.

24. What is the predicted miles per gallon for a car weighing 3100 pounds? • Less than 14.5 miles per gallon. • At least 14.5 miles per gallon, but less than 16.5 miles per gallon. • At least 16.5 miles per gallon, but less than 18.5 miles per gallon. • At least 18.5 miles per gallon, but less than 20.5 miles per gallon. • At least 20.5 miles per gallon.