QNT 351: Learning Teams Problem Sets
IMPORTANT:
Showing your work and how you reached the answer is critical in receiving your grade…simply putting down values as the final answer will not earn you any points.
Week 5 LT Assignments
1. The city council of Pine Bluffs is considering increasing the number of police in an effort to reduce crime. Before making a final decision, the council asked the chief of police to survey other cities of similar size to determine the relationship between the number of police and the number of crimes reported. The chief gathered the following sample information.
a. Which variable is the dependent variable and which is the independent variable? Hint: Which of the following makes better sense: Cities with more police have fewer crimes, or cities with fewer crimes have more police? Explain your choice.
b. Draw a scatter diagram.
c. Determine the correlation coefficient.
d. Interpret the correlation coefficient. Does it surprise you that the correlation coefficient is negative?
2. Pennsylvania Refining Company is studying the relationship between the pump price of gasoline and the number of gallons sold. For a sample of 20 stations last Tuesday, the correlation was .78. At the .01 significance level, is the correlation in the population greater than zero?
Yes
the correlation is 5.2882199918 this = 0.78 to the square root of (20-2 )/ the square Root of 1 – (0.78)^2
3. A study of 20 worldwide financial institutions showed the correlation between their assets and pretax profit to be .86. At the .05 significance level, can we conclude that there is positive correlation in the population?
· The correlation is positive
· T=0.86 square root of 20-2/ the square root of 5-(0.82)^2= 1.7539255221
4. The following sample observations were randomly selected.
Determine the correlation coefficient and interpret the relationship between x and y.
· Correlation coefficient= 0
€(X-x)(Y-y)/(n-1)(SxSy) = (0)(0)/(5-1)(1.968)(-0.377856) = 0
· Value of X = 5.6
4+5+3+6+10/5=5.6
· Value of Y= 5.8
4+6+5+7+7/5=55.8
· Value of S(x)=1.968
(X-x)^2/5=1.968
· Value. Of S(y)=-0.192
(Y-y)2/5=-0.192
5. Refer to the following table
Determine the correlation coefficient and interpret the relationship between x and y.
Correlation coefficient=
€(X-x)(Y-y)/(n-1)(SxSy) =0
0.125+-1.875+1.125-1.875-0.875-0.875+1.125+3.125=0(x-x) one zero in the above equation makes it total out at 0.
· Value of X =4.875
Add all x values and divide by 8
· Value of Y= 10.625
Add all y values and divide by 8
· Value of S(x)= 0.46875
(X-x)^2/5=0.46875
· Value Of S(y)= -1.87109315
(Y-y)2/5=-1.87109315
