type your answers in complete sentences and in the context of the question. To obtain full credit for your answer, show the major steps in your work or provide an explanation of how you obtained your answer.
1. Here are the numbers of emails that I received in 12 consecutive workdays.
22 35 23 44 18 25 29 24 22 22 44 19
(a) Use your calculator to compute the mean and the standard deviation of the number of emails. There is no need to show your calculations.[4 pts]
(b) Interpret the value of the standard deviation for a layperson.[4 pts]
(c) The largest number of emails is how many standard deviations above the mean?[4 pts]
2. During the last Presidential election a student in the Government Department at Simmons recorded the waiting time in line to vote for 30 voters. These times (in minutes) are summarized in the stemplot below
Stem-and-leaf of Wait N = 30
Leaf Unit = 1.0
8 0 00123344
(9) 0 555567889
13 1 0
12 1 5568
8 2 0013
4 2 5
3 3
3 3 89
1 4 5
(a) What are the ‘individuals’ in this case?
(b) What is the variable? Is it qualitative or quantitative?[3 pts]
(c) How would characterize the shape of the distribution?[4 pts]
(d) What fraction of the voters had to wait more than half an hour?[3 pts]
(e) Interpret (in context, please) the values 4 and (9) in the column to the left of the plot.[3 pts]
(f) Compute the median wait time.[5 pts]
(g) What is the IQR of wait times?[5 pts]
(h) Use the quartile-based method to determine if the data set contains any outliers. If you detect any outliers, identify them[6 pts]
3. State highway officials know that the distribution of automobile speed on the Massachusetts Turnpike between Worcester and Sturbridge is approximately Normal with a mean of 72 mph and a standard deviation of 6 mph. Explain using the Zscore method.
(a) What percentage of drivers exceed 80 mph?[4 pts]
(b) What is the 90thpercentile of speed on this stretch of the Turnpike?[4 pts]
(c) Use (only) you answer in part (b) to obtain the 10thpercentile of speed.[5 pts]
4. The following statements are either misleading or contain one or more errors relating to correlation. Point out what is misleading or the nature of the error(s).
(a) “For the 27 students in my Math 418 class last semester, the correlation between the score on the third exam and the score on the final exam was 1.03.”[3 pts]
(b) “ Among a sample of those completing the Boston Marathon in 2010, the correlation between age and speed was -0.567; the intercept of the corresponding regression line (predicting speed from age) is 9.5 and the slope,0.068.”[4 pts]
(c) “The correlation between the income and the race of 50 middle-aged lawyers is 0.67 dollars.”[5 pts]
(d) “Since the correlation coefficient between these two variables equals 0, there is no relationship between them.”[4 pts]
5. In a study at the Harvard Business School some years ago students were randomly divided into 13 groups of sizes ranging from 2 students to 12 students. Each group was separated from the others and each group was given the same set of facts about a management problem and were asked to reach a decision about which of four courses of action the management team should take. What interested the researcher in charge of the study was how the time to reach a decision varied with the size of the group. The scatterplot below is for decision time (in minutes) against the size of the group. Some relevant regression output is below the graph.
Regression Equation
DecTime = 13.86 + 8.94 SizeGroup
R-sq
81.75%
(a) What does the plot suggest about the relationship between these two variables?[3 pts]
(b) Interpret the slope of the regression line in this case.[5 pts]
(c) Use the equation of the regression line to predict the decision time for a new group made up of seven students.[3 pts]
(d) How much of the variability in decision time can be associated with differences in group size?[4 pts]
(e) What is the value for the correlation coefficient in this case?[6 pts]
(f) One SizeGroup is exactly 4 students and the DecTime was 50 minutes. What was the group residual? Write a sentence explaining to your friends what this residual means.[5 pts]
6. You are in a large statistics class and learn that you scored an 80 on the first exam. According to the instructor, the average score on the exam was 70. Would you be more satisfied if the standard deviation of scores was 5 points or if it was 15 points? Explain.[8 pts]