This report presents the statistics from the data supplied by the Ordinary People’s Bank. This report presents a number of key findings apart from presenting the summary statistics of all the key 6 variables. It is important to point out that random sample of 50 observation were selected and all the calculation was based on this sample observations.
The first variable for which we present the descriptive statistics is transaction (in whole dollars). The mean of the observation is 7,700 dollars. The median is 8,000 dollars. The mode is 10,000 dollars. The graphical representation has been presented in Appendix 1.
The next variable for which the summary account is presented is Open Account. Essentially, in my sample there were 5 individuals with accounts not opened whereas the remaining individuals totaling 45 had accounts opened. The graphical representation has been presented in Appendix 2.
The mean of balance in the dollars of the sample is 606.14. The median of the balance is 390. The mode of balance is 0. The graph of the Account balance in dollars has been presented in Appendix 3.
The mean age of the sample is 60 years. The median age of the sample is 61 years. The mode age of the sample is 51 years. The graph of the age has been presented in Appendix 4.
The sex of the sample has been categorized as 1 for males and 0 for females. The associated graph has been shown in the Appendix 5.
The type of account is characterized as 1 for Visa and 0 for both savings and cheque. The associated graph has been shown in Appendix 6 (Isotolo, n.d).
The average age of account holders for the open accounts only is 60 years. The lower bound of the age for 95% confidence interval is 56.33. The upper bound of the age for 95% confidence interval is 63.17. In other words, it can be said with 95% confidence that the average age of the true sample (which includes 1000 observation, in our case) lies between 56.33 and 63.17. The relevant calculation has been shown in Appendix 6 (Thompson, 2011).
The true mean of age from the full data is 58 years. Hence, the fact that the true mean falls within the confidence interval bounds is verified.
The average total transaction dollars for all accounts is 7,770. The lower bound of the total transaction dollars for 95% confidence interval is 6975.95. The upper bound of the total transaction dollar for 95% confidence interval is 8564. The relevant calculation has been shown in Appendix 7.
The true mean of total transaction from the full data is 8022 dollars. Hence, the fact that the true mean falls within the confidence interval bounds is verified (Reyna, 2010).
Difference of Mean for Account Balance between Male and Female
A hypothesis test was performed in order to test if there is a difference in mean value of accounts between male and female. The hypothesis clearly indicates that the mean value of account balance for both males and females is the same. More details are given in Appendix 8.
Difference of Mean for Average Transaction Dollar for Visa and Non-Visa
A hypothesis test was performed in order to test if there is a difference in mean value of average transaction dollar between Visa and Non-Visa. The hypothesis clearly indicates that the mean value of account balance for both Visa and Non-Visa is the same. More details are given in Appendix 9 (Paiva, n.d).
The scatterplot of the diagram has been displayed below. The x axis represents the age and Y axis represents the transaction.
The linear regression model will take the form given below
The coefficient of determination of this regression model is 47.20%. In other words, 47% of the variation in transaction is explained by age.
Age has negative relationship with transaction (in dollars). In other word, an increase in age by one unit decreases the transaction by 114.91 dollars. Essentially, decrease in age leads to an increase in transaction (in dollars). See Appendix 10 for the Output Table.
The coefficient of correlation is -0.47 between these two variables. See Appendix 11 for the Output Table.
The hypothesis that was conducted revealed that the coefficient is statistically different from zero. Check Appendix 12 for the Output Table (Anderson, 2000).
A number of key findings has been derived from the report. The most important finding was that age has negative relationship with transaction. The bank should make an attempt at finding out the reasons that leads to this negative relationship. In fact, the transaction of individuals should increase with age but in this case it does not.
Anderson, D., 2000. Null Hypothesis Testing. Problems, Prevalence and Alternatives. Journal of Wildlife Management, 64(4), pp. 912-923.
Isotolo, J., n.d. Basic Statistics. University of Helsinki, [online]. Available at: <https://www.mv.helsinki.fi/home/jmisotal/BoS.pdf> [Accessed 25 October 2016].
Paiva, A., n.d. Hyothesis Testing. University of Utah, [online]. Available at: <https://www.sci.utah.edu/~arpaiva/classes/UT_ece3530/hypothesis_testing.pdf> [Accessed 25 October 2016].
Reyna, O., 2010. Data Preparation and Descriptive Statistics. Princeton University, [online]. Available at: <https://www.princeton.edu/~otorres/DataPrep101.pdf> [Accessed 25 October 2016].
Thompson, G., 2011. Hypothesis Testing for Difference of Population Parameters. Hypothesis Test Difference, [online]. Available at: <https://wiki.stat.ucla.edu/socr/uploads/3/32/thomson_socr_econ261_hypothesisdifferencemeans_viii.pdf> [Accessed 25 October 2016].
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