Statistical Analysis of Bank in New Jersey - Statistics Project Example

MEMO Wednesday, February 17, FINRA XYZ Re: Evaluating Bank in New Jersey (Scatter Diagrams & Descriptive Statistics) INTRODUCTION Thank you for the opportunity to evaluate the factor, the percentage of the population in each county influencing the number of people in each county per branch bank in New Jersey. Every Financial institution has a legal and social responsibility to serve all communities and banks are obliged to serve adequately both inner-city and suburban neighborhoods, both poor and wealthy communities. A number of questions arise recently such as “Do New Jersey banks serve minority communities?” In New Jersey, banks have been charged with withdrawing from urban areas with a high percentage of minorities. To examine this charge, a regional New Jersey newspaper, Asbury Park Press, compiled county by county data on the number of people in each county per branch bank and the percentage of the population in each county that is considered minority. This data represent 21 New Jersey counties. This report will examine correctness of the charge that New Jersey banks have been withdrawing from urban areas with a high percentage of minorities. For this, I will use Asbury Park Press compiled county by county data and summarize this data set using scatter diagram and the descriptive statistics and presents findings in this memo. The importance of this study is to test whether banks serve their own communities. SCATTER DIAGRAM A scatterplot is created taking “x” as the percentage of the population within each county that is minority and “y” as people in each county per branch bank within the county. Figure 1 shows the scatter diagram of minority percentage (independent variable x) against the number of people per bank branch (dependent variable y). There appears a strong direct positive relationship between the number of people in county per branch bank and the percentage of minority population in county. The R2 value of 0.5265 indicates that about 52.65% of the variation in the number of people in county per branch bank is explained by the percentage of minority population in county. This is a strong effect. However, the other 47.35% of the variation in the number of people in county per branch bank remains unexplained. The regression equation is given by Number of People per Bank Branch = 2082 + 35.89 (Minority Percentage in County) The slope coefficient of regression of 35.89 suggests that for every percent increase in minority population in the county, the number of people per bank branch increases by about 36 on average. The intercept coefficient of regression of 2082 suggests that for no minority population in the county, the number of people per bank branch will be about 2,082 on average. A regression analysis was performed taking the percentage of minority population in the county as independent variable (x) and the number of people in county per branch bank as dependent variable (y). The p-value for “x” variable the percentage of minority population in the county is 0.0002, which is less than 0.01. Therefore, the percentage of minority population in the county significantly predicts the number of people in county per branch bank, t(19) = 4.60, p < .01. The result suggests that the charge that New Jersey banks have been withdrawing from urban areas with a high percentage of minorities is not correct. The reason for this is that as the percentage of minority population in the county increases, the number of people in county per branch bank also increases, which is contradictory of the allegation on the New Jersey banks. DESCRIPTIVE STATISTICS Table 1 shows the descriptive statistics for the percentage of minority population in the county (independent variable) and the number of people in county per branch bank (dependent variable). Table 1 – Descriptive Statistics   Minority Percentage Number Mean 17.32 2693.33 Standard Error 2.54 123.72 Median 16.70 2607 Standard Deviation 11.66 566.96 Sample Variance 135.92 321448.03 Kurtosis 1.06 0.24 Skewness 0.88 -0.36 Range 46.4 2362 Minimum 2.4 1321 Maximum 48.8 3683 Count 21 21 Coefficient of Variation (CV) 67.30% 21.05% Percentage of Minority Population in the County (Independent Variable) The average percentage of minority population in the county is about 17.32% (SD = 11.66%). The range of the percentage of minority population in the county is 46.4%. The minimum and maximum percentage of minority population in the county is 2.4% and 48.8%, respectively. A z-score analysis of the percentage of minority population in the county resulted in maximum z-score of 2.70 and minimum z-score of -1.28. These value are with-in interval |z| = 3, therefore, there are no outliers present in the percentage of minority population in the county data. A 2-standard interval of the percentage of minority population in the county is -5.99% to 40.64%. About 95.24% of the data values fall in this interval. Therefore, the 2-standard deviation interval for the percentage of minority populations in the county is in accordance with Chebyshev’s Rule (at least 75% data values within 2-standard deviation of the mean) and the Empirical Rule (approximately 95.44% data values of normal random variable within 2-standard deviation of the mean). Number of People per Bank Branch (Dependent Variable) The average number of people per bank branch in the county is about 2,693 (SD = 567). The range of the number of people per bank branch in the county is 2,362. The minimum and maximum number of people per bank branch in the county is 1,321 and 3,683, respectively. Coefficient of Variation (CV) Analysis The coefficient of variation (ratio of standard deviation divided by mean) indicates how large the standard deviation is in relation to the mean. The coefficient of variation (CV) for the percentage of minority population in the county is about 67.30% and for the number of people per bank branch in the county is about 21.05%. Therefore, the percentage of minority population in the county is more variables as compared to the number of people per bank branch in the county. The coefficient of variation (CV) for New York is 20%. This suggests that the percentage of minority population in the New Jersey is highly variable as compared to New Work. However, the number of people per bank branch in the New Jersey varies approximately same as New York. COnclusions Based on this analysis, here are some points that can assist you in examining how New Jersey banks serve minority communities. 1) There is a strong positive association between the percentage of minority population and the number of people per branch bank in New Jersey County. 2) The percentage of minority population in the county significantly predicts the number of people in county per branch bank in New Jersey, which is contradictory of the allegation on the New Jersey banks. 3) The average percentage of minority population in the county is about 17.32% (SD = 11.66%) with no outliers in the data. 4) The average number of people per bank branch in the county is about 2,693 (SD = 567 with no outliers in the data. 5) The percentage of minority population in the New Jersey is highly variable as compared to New Work In conclusion, I can say that New Jersey banks serve better where minority communities’ percentage is higher. Therefore, the charge that New Jersey banks have been withdrawing from urban areas with a high percentage of minorities is baseless. Thank you again for the opportunity to research the factor, the percentage of the population in each county influencing the number of people in each county per branch bank in New Jersey. If you have any questions, please contact me. Thank you, REGARDS, STUDENT XYZ, Statistics Student Dominican University Attachments Table 2: Regression Analysis SUMMARY OUTPUT Regression Statistics Multiple R 0.7256 R Square 0.5265 Adjusted R Square 0.5016 Standard Error 400.2546 Observations 21 ANOVA   df SS MS F Significance F Regression 1 3385090 3385090 21.1299 0.0002 Residual 19 3043870 160203.7 Total 20 6428961         Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 2082.0153 159.1070 13.0856 0.0000 1749.0005 2415.0301 PctMinority 35.2877 7.6767 4.5967 0.0002 19.2202 51.3553 Table 3: z-score Analysis and 2-Standard Deviation Interval PctMinority (Z-score) Number (Z-score) Max 2.700 1.746 Min -1.280 -2.421 PctMinority Number Mean - 2 Standard Deviation -5.99 1559.41 Mean 2 Standard Deviation 40.64 3827.26 Number of Values 20 20 % of Values 95.24% 95.24% Read More