Case Study National Century Bank free essay sample

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 Interpret the results. SOLUTION 95% confidence interval = 5% significance level Level of significance, ? = 0. 05 ; Z (? /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 customers use debit card. QUESTION 2 With many other options available, customers no longer let their money sit in a checking account. For many years the mean checking balance has been $1600. Does the sample data indicate that the mean account balance has declined from this value? SOLUTION  µ (Checking balance) = 00. We will write a custom essay sample on Case Study National Century Bank or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page 00 Number of customers, n = 60 In this case, level of significance, ? was not provided. Therefore, the analysis will be evaluated based on two ? values which are: ? = 0. 05; Z? = 1. 65 ? = 0. 01; Z? = 2. 33 Hypotesis testing 1) H0 :  µ ? 1600 H1 :  µ lt; 1600 2) ? = 0. 05 ? = 0. 01 3) Left-tail test Z(0. 05) = 1. 65 Z(0. 01) = 2. 33 4) Z calculated :- -1. 65 -2. 33 ?=0. 05 ?=0. 01 Z= -1. 2994 5) From calculations, computed z value is more than -1. 65 and falls within Ho not rejected region. Ho is not rejected at ? = 0. 05 amp; ? = 0. 01 ignificance levels. It is concluded that the mean checking balance is still similar or more than $1600 QUESTION 3 Recent years have also seen an increase in the use of ATM machines. When Mr. Selig took over the bank, the mean number of transactions per month per customer was 8; now he believes it has increased to more than 10. In fact, the advertising agency that prepares TV commercial for Century would like to use this on the new commercial being designed. Is there sufficient evidence to conclude that the mean number of transactions per customer is more than 10 per month? Could the advertising agency say the mean is more than 9 per month? SOLUTION The following question requires hypothesis testing for 2 sets of  µ. Test 1 will measure whether the mean number of transactions per month per customer is greater than 9. Test 2 will measure whether the number of transactions per month per customer is greater than 10.  µ (Test 1) = 9 ;  µ (Test 2) = 10 n = 60 ? = 0. 05; Z? = 1. 65 ? = 0. 01; Z? = 2. 33 Hypotesis testing (Test 1) 1) H0 :  µ = 9 H1 :  µ gt; 9 2) ? = 0. 05 ? = 0. 01 3) Right-tail test Z(0. 05) = 1. 65 Z(0. 01) = 2. 33 4) Z calculated :- Z= 2. 3445 2. 33 1. 65 ?=0. 01 ?=0. 05 5) From calculations, computed z value is more than 2. 33 and falls within Ho rejected region. Ho is rejected at ? = 0. 05 amp; ? = 0. 01 significance levels. It is concluded that the mean number of transactions per month per customer is greater than 9. Therefore, the advertising agency can say the mean is more than 9 per month Hypotesis testing (Test 2) 1) H0 :  µ = 10 H1 :  µ gt; 10 2) ? = 0. 05 ? = 0. 01 3) Right-tail test Z(0. 05) = 1. 65 Z(0. 01) = 2. 33 4) Z calculated :- ?=0. 05 ?=0. 01 Z= 0. 5410 1. 65 2. 33 5) From calculations, computed z value is less than 1. 65 and falls within Ho not rejected region. Ho is not rejected at ? = 0. 05 amp; ? = 0. 01 significance levels. It is concluded that the mean number of transactions per month per customer is similar to 10. Therefore, there is not sufficient vidence to conclude that the mean number of transactions per customer is more than 10 per month QUESTION 4 Refer to the Century National Bank data. Is it reasonable that the distribution of checking account balances approximates a normal probability distribution? Determine the mean and the standard deviation for the sample of 60 cust omers. Compare the actual distribution with the theoretical distribution. Cite some specific examples and comment on your findings. SOLUTION Number of customers, n = 60 Actual distribution: Balance| Freq| Relative Freq| 0 up to 421| 4| 0. 0667| 422 up to 843| 6| 0. 1| 844 up to 1264| 8| 0. 1333| 1265 up to 1685| 16| 0. 2667| 1686 up to 2106| 16| 0. 2667| 2107 up to 2527| 9| 0. 15| 528 up to 2948| 1| 0. 0167| Total| 60| 1| The following table above was extracted from the sample set of data. From the graph above, it can be seen that the distribution of the checking account balances approximates a normal probability distribution. Comparison of actual distribution with theoretical distribution:- * Actual distribution: Class ($1686 up to $2106) = 0. 2667 (relative frequency) * Theoretical distribution: Using Z formula:- For X = 1686For X = 2106 P (between $1686 and $2106) = 0. 3531 – 0. 1255 = 0. 2276 From the example taken (between $1686 and $2106), it can be seen that there is s ome difference in the probability calculated. Actual distribution yields the probability value of 0. 2667 whereby theoretical distribution yields the value 0. 2276. Margin of error is to be expected considering the large sample size. The probability of the sample size is to give a rough estimate on the actual values. QUESTION 5 Divide the account balances into three groups, of about 20 each, with the smallest third of the balances in the first group, the middle third in the second group, and those with the largest balance in the third group. Next, develop a table that shows the number in each of the categories of the account balances by branch. Does it appear that account balances are related to the branch? From this table, it indicates that the categories of account balances (smallest, middle and largest balance) are related to the branch. This is because smallest amount of account balances was mostly deposited in Branch 1 (Cincinnati, Ohio) and largest amount of account balances was mostly deposited in Branch 2 (Atlanta, Georgia). CONCLUSION 1. Based on the sample data, at 95% confidence level, it can be concluded that more than 50% of the customers use the debit card. 2. The mean checking balance for Century National Bank is concluded to be similar or more than $1600 which is almost same for many years. 3. The mean number of transactions per month per customer is concluded to be greater than 9. Therefore, the advertising agency can say the mean is more than 9 per month. But, there is no sufficient evidence to conclude that the mean is more than 10 per month. 4. There is some difference in the probability calculated. Actual distribution yields the probability value of 0. 2667 whereby theoretical distribution yields the value 0. 2276. Margin of error is to be expected considering the large sample size. 5. It can be concluded that the categories of account balances (smallest, middle and largest balance) are related to the branch.