Century National Bank x1 - Account Balancex2 - Number of ATM x3 - Number of otherx4 - Has a debit cardx5 - Receives interestx6 - City x1 - Account Balance in $ 1,756134012 x2 - Number of ATM...

Table of Contents
Introduction    2
Analysis    2
Conclusion    3
References    4
Appendix    4
Introduction
It is required to estimate the proportion of all customers of century national bank who use debit card. The technique of confidence intervals is used here. The objective is to test if more than 50% customers of century national bank use debit card.
Analysis
The variable X4 denotes if the customer has a debit card. It is given the value of 1 if he has a debit card and 0 if he doesn’t have a debit card.
Let X represent the number of customers using cards. This is calculated with the sum of 1’s for the variable X4.
Let n represent the total number of customers. This is equivalent to 60.
Let P-hat represent the proportion of customers using cards. Mathematically, P-hat = X/n = 26/60= 0.43
Then X follows Binomial distribution with n=60 and p=0.43.
The conditions for normal approximation to binomial are that np>=5 and nq >=5. Wilcox, R. R. (2011). In this case, the np = 60*0.43 = 26 and nq = 60*(1-.43) = 34.
Hence, I can say that X is normally distributed with mean = np and variance = npq. In this case, mean = E(X) = np = 60*0.43 = 26
variance = V(X) = npq = 60*0.43*(1-0.43) = 14.706
The confidence interval for z test of one sample proportions is given by:
Confidence interval = p +- z(a/2)*sqrt(p*(1-p)/n)
Critical value, z(a/2) = z(0.05/2) = 1.96
Lower Limit = 0.433-1.96*SQRT(0.433*(1-0.433)/60) = 0.308
Upper Limit =...