statistics b3

Section 9.1

1.  True or False? -0.835 is a valid value for the correlation coefficient, rr.

2. Using the scatter plot in Figure 1 below, determine whether there is a positive linear correlation, negative linear correlation, or no linear correlation between the variables.

Figure 1. Scatter Plot

Problems 3-5

Instructions Use the data sets in Table 1 to answer the questions.

The data in Table 1 are the magnitude of an earthquake, xx, related to the depth below the surface, yy, at which the quake occurs.

Table 1. Depth of Earthquakes
Magnitude xx	Depth yy
2.9	5.0
4.2	9.9
3.3	11.3
4.5	10.0
2.6	4.8
3.1	3.9
3.5	5.5

3. Display the data in a scatter plot. ( Please, orient the x and y-axes in the usual way.)

4. Calculate the correlation coefficient, rr ( Note: use technology; round result to 3 decimal places.).

5. What do you conclude about the type of correlation?

Problems 6-8

Instructions Use the data sets in Table 2 to answer the questions.

College Crime. Do larger universities tend to have more property crime? Let xx be the student enrollment (in thousands) and yy be the number of burglaries in one year. ( Please, orient the xx and yy-axes in the usual way.)

Table 2. Property Crime at Universities
Enrollment (in thousands) xx	Burlaries yy
12.4	26
31.0	73
24.6	38
14.2	24
7.6	15
27.7	31
16.3	18
20.1	25

6. Display the data in a scatter plot. ( Please, orient the x and y-axes in the usual way.)

7. Calculate the correlation coefficient, rr ( Note: use technology; round result to 3 decimal places.).

8. What do you conclude about the type of correlation?

Section 9.2

9. Besides graphing, what is an important use for the equation of a regression line?

Problems 10-13

Instructions Use the data sets in Table 3 to answer the questions.

Auto Accidents and Age. Let xx be the age of a licensed driver (in years). Let yy be the percentage of all fatal accidents for a given age due to failure to yield the right of way.

Table 3. Failure to Yeld Right of Way
Age (years) xx	Percentage of All Fatal Accidents yy
37	5
47	9
57	10
67	15
78	29
86	43

10. What is the equation of the regression line (Round the coefficients to 3 decimal places.)?

11. Construct a scatter plot for the data showing the regression line  and the data points on the same graph. (See FAQ Chapter 5)

Problems 12-13

Use the regression equation found in question 10 to predict the values of yy for the values of xx given. If it is not meaningful to predict the value of yy, state that.

12. x=60x=60

13. x=30x=30

Section 3.1

Problem 14

Instructions Use the following information to solve the problem.

Spinner and coin probability experiment. A probability experiment is conducted by first spinning the spinner shown in Figure 2, then tossing a coin. Assume the results of the spin and the coin toss are free from bias.

Figure 2. Spinner

14. Draw a tree diagram for the probability experiment. If you decide to use MS Excel, see FAQ 5.9.

Problem 15

Instructions Use the information given for the event below to solve the problem.

A computer is used to randomly select a number between 1 and 2000. Event AA is selecting a number greater than 1700.

15. Is event AA a simple event (Yes or No)? Explain your answer.

16.  Multiple Choice Quiz. A multiple choice quiz has four possible answers per question. Assuming that no questions are left unanswered, in how many different ways can a 10 question multiple choice quiz be answered?

Section 3.2

17.  Probability Experiment. A probability experiment consists of spinning the spinner used in problem 14 and rolling a six-sided die. What is the probability of spinning an even number and then rolling an odd number greater than 2?

18.  Use the frequency distribution in Table 4. What is the probability that a voter chosen at random is between 21 and 44 years old? (Round results to 3 decimal places.)

Table 4. Ages of Voters
Ages of Voters	Frequency (In millions)
18 to 20 years old	5.8
21 to 24 years old	8.5
35 to 44 years old	21.7
45 to 64 years old	51.7
65 years old and over	26.7

19.  Use the pie chart in Figure 3 to find the probability. What is the probability that a student attained C or less on the quiz?

Figure 3. The grades attained by students on a recent quiz.

Problems 20-21

Instructions Use the information below to answer the questions.

Pickup Trucks. In a survey, 840 adults were asked if they drive a pickup truck and if they drive a Ford. The results showed that one in 7 adults surveyed drives a pickup truck, and two in eleven adults surveyed drives a Ford. Of the adults surveyed that drive Fords, two in nine drive a pickup truck.

20. Find the probability that a randomly selected adult drives a Ford and drives a pickup truck.

21. Are the events driving a Ford and driving a pickup truck independent or dependent ? ( Note: You must show the calculations needed to justify your decision to obtain full credit.)

Problems 22-25

Use the information in Table 5 to answer the questions. Round results to 3 decimal places. The table shows the number of male and female students enrolled in Nursing at a university in a recent semester.

Table 5. Students Enrolled in Nursing
	Nursing Majors	Non-Nursing Majors	Total
Males	121	1197	1318
Females	732	1458	2190
Total	853	2655	3508

22. Find the probability that a randomly selected student is a nursing major.

23. Find the probability that a randomly selected student is a nursing major given that the student is a male.

24. Find the probability that a randomly selected student is a nursing major and male.

25. Are the events being a male student and being a nursing major independent or dependent events? Show the probability calculations needed to support your answer to get full credit.