For each of 200 randomly selected cities, Pete compared data for the number of churches in the city (x) and the number of homicides in the past decade (y).
He calculated the linear correlation coefficient and was surprised to find a strong positive linear correlation for the two variables. Does this suggest that when a city builds new churches this will tend to cause an increase in the number of homicides? Why do you think that a strong positive linear correlation coefficient was obtained?
Q. 2Given a group of students: Allen (A), Brenda (B), Chad (C), Dorothy (D), and Eric (E), list all of the possible samples (without replacement) of size four that can be obtained from the group.
A) A,B,C,D
B) A,B,C,D A,B,C,E A,C,D,E A,D,E,B B,C,D,E B,C,E,A B,D,E,A
C,A,B,D C,E,D,B D,A,C,E
C) A,B,C,D A,B,C,E A,C,D,E A,D,E,B
D) A,B,C,D A,B,C,E A,C,D,E A,D,E,B B,C,D,E
Q. 3The age distribution of students at a community college is given below.
Age (years) Number of students (f)
Under 21 4946
21-25 4808
26-30 2673
31-35 2036
Over 35 525
A student from the community college is selected at random. The event A is defined as follows.
A = event the student is between 26 and 35 inclusive.
Describe the event (not A) in words.
A) The event the student is over 35 B) The event the student is under 26 and over 35
C) The event the student is at most 26 or at least 35 D) The event the student is under 26 or over 35
Q. 4At one hospital in 1992, 674 women were diagnosed with breast cancer. Five years later, 88 of the Caucasian women and 63 of the African American women were still alive.
This observational study shows an association between race and breast cancer survival--that Caucasian women are more likely to survive breast cancer than African American women. How could this study be modified to make it a designed experiment? Comment on the feasibility of the designed experiment that you described.
Q. 5Which of the following statements concerning the linear correlation coefficient are true?
A: If the linear correlation coefficient for two variables is zero, then there is no relationship between the variables.
B: If the slope of the regression line is negative, then the linear correlation coefficient is negative.
C: The value of the linear correlation coefficient always lies between -1 and 1.
D: A linear correlation coefficient of 0.62 suggests a stronger linear relationship than a linear correlation coefficient of -0.82.
A) B and C B) C and D C) A and D D) A and B
Q. 6Why do statisticians sometimes use inferential statistics to draw conclusions about a population? In what situations might a statistician draw conclusions about a population using descriptive statistics only?
What will be an ideal response?
Q. 7The variables height and weight could reasonably be expected to have a positive linear correlation coefficient, since taller people tend to be heavier, on average, than shorter people.
Give an example of a pair of variables which you would expect to have a negative linear correlation coefficient and explain why. Then give an example of a pair of variables whose linear correlation coefficient is likely to be close to zero.
Q. 8Define observational study and designed experiment.
What will be an ideal response?
Quick Reply
