Case Study National Century Bank

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TABLE OF CONTENT

1| Introduction| 2|
2| Question 1| 3|
3| Question 2| 4|
4| Question 3| 6|
5| Question 4| 9|
6| Question 5| 11|
7| Conclusion| 12|

INTRODUCTION
Century National Bank has offices in several cities in the Midwest and the southeastern part of the United States. Mr. Dan Selig, president and CEO, would like to know the characteristics of his checking account customer. To better understand the customers, Mr. Selig asked Ms. Wendy Lamberg, director of planning, to select a sample of customers and prepare a report. To begin, she has appointed a team from her staff and the team has selected a random sample of 60 customers. All the information gathered is tabulated in the table below: X1 = Account balance in $| X4 = Has a debit card (1 = yes, 0 = not)| X2 = Number of ATM transactions in the month| X5 = Receives interest on the account (1 = yes, 0 = not)| X3 = Number of other bank services used| X6 = City where banking is done|

No.| X1| X2| X3| X4| X5| X6| No.| X1| X2| X3| X4| X5| X6| 1| 1756| 13| 4| 0| 1| 2| 31| 1958| 6| 2| 1| 0| 2| 2| 748| 9| 2| 1| 0| 1| 32| 634| 2| 7| 1| 0| 4| 3| 1501| 10| 1| 0| 0| 1| 33| 580| 4| 1| 0| 0| 1| 4| 1831| 10| 4| 0| 1| 3| 34| 1320| 4| 5| 1| 0| 1| 5| 1622| 14| 6| 0| 1| 4| 35| 1675| 6| 7| 1| 0| 2| 6| 1886| 17| 3| 0| 1| 1| 36| 789| 8| 4| 0| 0| 4| 7| 740| 6| 3| 0| 0| 3| 37| 1735| 12| 7| 0| 1| 3| 8| 1593| 10| 8| 1| 0| 1| 38| 1784| 11| 5| 0| 0| 1| 9| 1169| 6| 4| 0| 0| 4| 39| 1326| 16| 8| 0| 0| 3| 10| 2125| 18| 6| 0| 0| 2| 40| 2051| 14| 4| 1| 0| 4| 11| 1554| 12| 6| 1| 0| 3| 41| 1044| 7| 5| 1| 0| 1| 12| 1474| 12| 7| 1| 0| 1| 42| 1885| 10| 6| 1| 1| 2| 13| 1913| 6| 5| 0| 0| 1| 43| 1790| 11| 4| 0| 1| 3| 14| 1218| 10| 3| 1| 0| 1| 44| 765| 4| 3| 0| 0| 4| 15| 1006| 12| 4| 0| 0| 1| 45| 1645| 6| 9| 0| 1| 4| 16| 2215| 20| 3| 1| 0| 4| 46| 32| 2| 0| 0| 0| 3| 17| 137| 7| 2| 0| 0| 3| 47| 1266| 11| 7| 0| 0| 4| 18| 167| 5| 4| 0| 0| 4| 48| 890| 7| 1| 0| 1| 1| 19| 343| 7| 2| 0| 0| 1| 49| 2204| 14| 5| 0| 0| 2| 20| 2557| 20| 7| 1| 0| 4| 50| 2409| 16| 8| 0| 0| 2| 21| 2276| 15| 4| 1| 0| 3| 51| 1338| 14| 4| 1| 0| 2| 22| 1494| 11| 2| 0| 1| 1| 52| 2076| 12| 5| 1| 0| 2| 23| 2144| 17| 3| 0| 0| 3| 53| 1708| 13| 3| 1| 0| 1| 24| 1995| 10| 7| 0| 0| 2| 54| 2138| 18| 5| 0| 1| 4| 25| 1053| 8| 4| 1| 0| 3| 55| 2375| 12| 4| 0| 0| 2| 26| 1526| 8| 4| 0| 1| 2| 56| 1455| 9| 5| 1| 1| 3| 27| 1120| 8| 6| 1| 0| 3| 57| 1487| 8| 4| 1| 0| 4| 28| 1838| 7| 5| 1| 1| 3| 58| 1125| 6| 4| 1| 0| 2| 29| 1746| 11| 2| 0| 0| 2| 59| 1989| 12| 3| 0| 1| 2| 30| 1616| 10| 4| 1| 1| 2| 60| 2156| 14| 5| 1| 0| 2| QUESTION 1

Refer to the description of the Century National Bank at the end of Review pf Chapters 1-4 page 136. When Mr Selig took over as president of Century several years ago, the use of debit cards was just beginning. He would like an update on the use of these cards. Develop a 95 percent confidence interval for the proportion of customers using these cards. On the basis of the confidence interval, is it reasonable to conclude that more than half of the customers use a debit card? Interpret the results. SOLUTION

95% confidence interval = 5% significance level
Level of significance, α = 0.05 ; Z (α/2) = ± 1.96
Number of customers, n = 60
P (Use debit card) = 26/60 = 0.433
Confidence interval formula:

From calculations, it was found that proportion value, P = 0.433 lies within confidence interval endpoints between 0.308 and 0.558. Based on the results, we can conclude that at 95% confidence level, more than 50% of National Bank...
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