14-8. Because of the current concern over credit card balances, a bank’s Chief Financial Officer is interested in whether there is a relationship between account balances and the number of times a card is used each month. A random sample of 50 accounts was selected. The account balance and the number of charges duringConstruct a scatter plot for these data and describe what, if any, relationship appears to exist between these two variables.

b.          Calculate the correlation coefficient for these two variables and test to determine whether there is a significant correlation at the a = 0.05 level.

14-10. Amazon.com has become one of the most successful online merchants. Two measures of its success are sales and net income/loss figures (all figures in

$million). These values for the years 1995–2007 are shown as follows.

 

Year                Net Income/Loss                     Sales

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

the past month were the two variables recorded. The correlation coefficient for the two variables was -0.23. 1995 -0.3 0.5 a. Discuss what the r = -0.23 measures. Make sure 1996 -5.7 15.7   to frame your discussion in terms of the two 1997 -27.5 147.7   variables mentioned here. 1998 -124.5 609.8 b. Using an a = 0.10 level, test to determine whether 1999 -719.9 1,639.8   there is a significant linear relationship between 2000 -1,411.2 2,761.9   account balance and the number of card uses 2001 -567.3 3,122.9   during the past month. State the null and alternative 2002 -149.1 3,933   hypotheses and show the decision rule. 2003 35.3 5,263.7 c. Consider the decision you reached in part b. 2004 588.5 6,921   Describe the type of error you could have 2005 359 8,490   made in the context of this problem. 2006 190 10,711

14-9. Farmers National Bank issues MasterCard credit cards to its customers. A main factor in determining whether a credit card will be profitable to the bank is the average monthly balance that the customer will maintain on

 

the card that will be subject to finance charges. Bank analysts wish to determine whether there is a relationship between the average monthly credit card balance and the income stated on the original credit card application form. The following sample data have been collected from existing credit card customers:

 

   2007                              476                            14,835       

 

a.     Produce a scatter plot for Amazon’s net income/loss and sales figures for the period 1995 to 2007. Does there appear to be a linear relationship between these two variables? Explain your response.

b.    Calculate the correlation coefficient between Amazon’s net income/loss and sales figures for the period 1995 to 2007.

c.    

Income CreditBalance and sales fi   $43,000 $345 assume tha t these figures form a random sa mple. $35,000 $1,370 14-11. Complaints concerning excessive commercia ls seem t $47,000 $1,140 grow as the amount of “ clutter,” including co mmercia $55,000 $201 and advertisements for other telev ision shows, steadil $55,000 $56 increases on network an d cable television. A recent $59,000 $908 analysis by Nielsen Monitor-Plus compares t he $28,000 $2,345 average nonprogram mi nutes in an hour of prime time $43,000 $104 for both network and ca ble televis ion. Data for selecte $54,000 $0 years are shown as follo ws.     $36,000 $1,290           $39,000 $130 Year 1996 1999 2001 2004 $31,000 $459 Network 9.88 14.00 14.65 15.80 $30,000 $0 Cable 12.77 13.88 14.50 14.92 $37,000 $1,950

Conduct a hypothesis test to determine if a positive correlation exists between Amazon’s net income/loss

 

gures. Use a significance level of 0.05 and

 

o ls y

 

 

 

 

d

 

 

 

 

 

 

 

 

 

 

a.     Indicate which variable is to be the independent variable and which is to be the dependent variable in the bank’s analysis and indicate why.

a.     Calculate the correlation coefficient for the average nonprogram minutes in an hour of prime time between network and cable television.

b.    Conduct a hypothesis test to determine if a positive correlation exists between the average nonprogram

 

 

 

minutes in an hour of prime time between network and cable television. Use a significance level of 0.05 and assume that these figures form a random sample.