Who know about statistics

Z-Test Three Rivers Bank

J. P. Getty

QNT 275 I5

January 3, 2017

Dr. Stephen Loro

Table of Contents

Introduction 3

Research Problem 3

Purpose of Study 3

Research Question 3

Null and Alternative Hypothesis 3

Alpha Level of Significance 3

Variable Definitions 3

Limitations 4

Review of Related Literature 4

Background 4

Methodology 4

Research Design 4

Data Collection 4

Data 5

Descriptive Statistics 6

Data Analysis 7

Statistical Methods 8

Results 8
Conclusions and Recommendations 9

References 10

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: μ1 = μ2

Alternative Hypothesis:

H1: There is a significant difference in ATM transactions from ATM machine One and ATM machine Two. H1: μ1 ≠ μ2

Alpha Level of Significance

The alpha level to be used is .05. as determined by management. (α = .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.

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.

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

	ATM 1	ATM 2
count	30	30
mean	123.93	126.57
sample standard deviation	20.50	19.45
sample variance	420.20	378.32
minimum	88	88
maximum	155	152
range	67	64

standard error of the mean	3.74	3.55

confidence interval 95.% lower	116.60	119.61
confidence interval 95.% upper	131.27	133.53
margin of error	7.34	6.96
	1.96	1.96

skewness	-0.09	-0.58
kurtosis	-1.33	-0.78
coefficient of variation (CV)	16.54%	15.37%

normal curve GOF
p-value	.1328	.3080
chi-square(df=3)	5.600	3.600
	5.000	5.000
O(-0.97)	8	6
O(-0.43)	3	3
O(+0.00)	4	3
O(+0.43)	4	5
O(+0.97)	3	8
O(inf.)	8	5

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.

Results

Hypothesis Test: Independent Groups (z-test)

	Raw Data	Group 2
	123.93	126.57	mean
	20.50	19.45	std. dev.
	30	30

		-2.633	difference (Raw Data - Group 2)
		5.159	standard error of difference
			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).

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