1 Z-Test Three Rivers Bank J. P. Getty QNT 275 I5 January 3, 2017 Dr. Stephen Loro Table of Contents I. Introduction 3 Research Problem 3 Purpose of Study 3 Research Question 3 Null and Alternative Hypothesis 3 Alpha Level of Significance 3 Variable Definitions3 Limitations 4 II. Review of Related Literature 4 Background 4 III. Methodology 4 Research Design 4 Data Collection 4 Data 5 Descriptive Statistics Data Analysis 6 7 Statistical Methods 8 IV. V. Results 8 Conclusions and Recommendations 9 References 10 I. Introduction Three Rivers Bank is a California bank that has installed two ATM machines. The bank managers would like to monitor the efficiency of these machines to provide better customer service. Research Problem ATM transactions may vary between machines due to performance at the Three Rivers Bank which may lead to customer dissatisfaction and loss of profits. Purpose of the Study To provide information to Three Rivers Bank management so they may make more informed decisions. Research Question Is there a significant difference in transactions between ATM machine #1 and ATM machine #2 over the course of 30 days? Null and Alternative Hypothesis Null Hypothesis: Ho: There is no significant difference in ATM transactions from ATM machine One and ATM machine Two. Ho: 1 = 2 Alternative Hypothesis: H1: There is a significant difference in ATM transactions from ATM machine One and ATM machine Two. H1: 1 2 Alpha Level of Significance The alpha level to be used is .05. as determined by management. ( = .05). Variable Definitions The measured variable represents a transaction by a bank customer at one of two ATM machines at Three Rivers Bank. The data is quantitative, discrete and ratio. Limitations This research was limited Three Rivers Bank ATM machines for 30 days in July 2016. The sample size was limited to 60 transactions, 30 from ATM machine 1 and 30 from ATM machine 2. The instrument of measurement was the ATM machine. II. Review of Related Literature Background Three Rivers Bank has been in business since 1849 at the junction of the three forks of the Yuba River in the Serria Nevada Mountains of California. Since the gold rush days Three Rivers Bank has been servicing customers with all banking needs. Three Rivers Bank has installed two ATM machines and management is interested in how they are being used by customers. III. Methodology Research Design The research design for this study was quasi-experimental random by occurrence. Data Collection Samples were the recording of customer transactions at two ATM machines. MegaStat was used to conduct the analysis. Data ATM 1 ATM 2 100 115 130 120 125 131 88 114 96 88 112 96 150 132 147 143 111 121 142 135 96 95 155 130 137 145 144 152 98 100 101 136 120 127 150 152 151 140 100 99 115 143 128 132 120 152 116 113 122 125 139 140 130 148 100 92 145 135 150 146 Descriptive statistics count mean sample standard deviation sample variance minimum maximum range standard error of the mean confidence interval 95.% lower confidence interval 95.% upper margin of error z skewness kurtosis coefficient of variation (CV) normal curve GOF p-value chi-square(df=3) E O(-0.97) O(-0.43) O(+0.00) O(+0.43) O(+0.97) O(inf.) ATM 1 30 123.93 20.50 420.20 88 155 67 3.74 116.60 131.27 7.34 1.96 -0.09 -1.33 16.54% ATM 2 30 126.57 19.45 378.32 88 152 64 3.55 119.61 133.53 6.96 1.96 -0.58 -0.78 15.37% .1328 5.600 5.000 8 3 4 4 3 8 .3080 3.600 5.000 6 3 3 5 8 5 Runs Plot 180.00 160.00 140.00 120.00 100.00 ATM 1 80.00 60.00 40.00 20.00 0.00 Transactions Runs Plot 160.00 140.00 120.00 100.00 ATM 2 80.00 60.00 40.00 20.00 0.00 Transactions Data Analysis The amount of ATM transactions recorded for machine One was 30. The mean or average of transactions made per day for machine one was 123.93. The sample standard deviation of 20.50 and the sample variance was 420.20. The minimum was 88 and the maximum was 155 with a range of 67. The standard error of the mean was 3.74. The lower 95% confidence limit was 116.60 and the upper 95% confidence limit was 131.27. The skew was -.09 and kurtosis -1.33. Coefficient of variation was 16.54%. The amount of ATM transactions recorded for machine Two was 30. The mean or average of transactions made per day for machine one was 126.57. The sample standard deviation of 19.45 and the sample variance was 378.32. The minimum was 88 and the maximum was 152 with a range of 64. The standard error of the mean was 3.55. The lower 95% confidence limit was 119.61 and the upper 95% confidence limit was 133.53. The skew was -.58 and kurtosis -.78 Coefficient of variation was 15.37%. A Goodness of Fit (GOF) test was conducted and determined that both the data sets were normally distributed (p=.13 and p=.30). Statistical Methods A two sample Z-test was conducted on the data to determine if there was a significant difference between the two machines as measured by transactions. A Z-test assumes a normal distribution and has 30 or more samples. MegaStat was used to conduct the analysis. IV. Results Hypothesis Test: Independent Groups (z-test) Raw Data Group 2 123.93 126.57 mean 20.50 19.45 std. dev. 30 30 n -2.633 difference (Raw Data - Group 2) 5.159 standard error of difference 0 hypothesized difference -0.51 z .6098 p-value (two-tailed) Retain the null hypothesis at the .05 alpha level of significance that there is no difference between the means of the machine transactions at Three Rivers Bank (p=.609). V. Conclusions and Recommendations There is no difference between the means of the machine transactions at Three Rivers Bank. We recommend that Three Rivers Bank should continue to provide customers with ATM service with the two machines and consider installing a third machine in the future. References Loro, S. (2017). Course Syllabus QNT 275 Statistics for Decision Making. University of Phoenix