Testing Statistical Hypothese Regression Analysis †MyAssignmenthelp.c

Question: Discuss about the Testing Statistical Hypothese Regression Analysis. Answer: Introduction One of the largest networks in the world in retail electronic payments is operated by the company Visa Inc. The company is also one of the most recognized brands in financial services across the world. The company provides a lot of facilities to the global commerce. These facilities include information and value transfer within some financial institutions, consumers, businesses, merchants and government entities management. There are a lot of types of fraud cases that are going on in the world nowadays. The most frequent fraud case that is happening now is credit card fraud. This type of card fraud is happening online as well as offline. Thus, this credit card company Visa Inc. is running this research to identify some specific issues and reduce the frequency of card fraud. The primary objectives of this research are discussed as follows. To identify whether the number of card fraud is experienced differs across gender. To identify whether there is any difference across age group of people regarding card fraud. To determine whether the average time that is required to resolve the problem of card fraud is less than 12 hours or not. To determine the frequency of occurrence of online or offline card fraud. To determine whether there is any difference between the frequency of online and offline card fraud. To identify the influence of customers satisfaction scores of response time, the level of advice and the level of communication on the overall satisfaction with the credit card fraud resolution team. Research Design In order to perform this research, data has to be collected. The data that is collected is on the experience of the customers in personal fraud. 2000 customers were selected randomly using the technique of simple random sampling. Among these 2000 customers who were selected to fill the questionnaire, 420 only responded. Thus, the success rate of the responses is only 21 percent. The ethical considerations that has to be kept in mind while collecting the data and doing the research are given below (Cacciattolo, 2015): The participants involved in the research should not be subjected to any types of harm. Respect and priority should be given to the dignity of the participants involved in the research. The participants should give full consent before participating in the study. The privacy of the participants taking part in the research must be assured. The data collected for the research purpose should be kept confidentially and must not be disclosed to anybody other than the individuals who are directly related to the research. . The participants of the survey must be assured that their identities will not be disclosed anywhere. The research aims and objectives must not be exaggerated. Any affiliations that are offered to the research or any sources from which the funding for the research are obtained must be mentioned at the time of the research. Communications that are necessary in doing the research must be done honestly and transparently. Information that are misleading to the research and biasness of the data in analysis and representation must not be done. For the purpose of the research, the following hypothesis can be framed: Is the number of card fraud experienced the same across gender? Null Hypothesis (H01): There is no significant difference between the card fraud experienced by males and females. Alternate Hypothesis (HA1): There is significant difference between the card fraud experienced by males and females. Are there differences across age groups regarding card fraud? Null Hypothesis (H02): There is no significant difference across age groups regarding card fraud. Alternate Hypothesis (HA2): There is no significant difference across age groups regarding card fraud. 12 hours time significant as response time compared to what the customers have experienced before? Null Hypothesis (H03): There is no significant difference in the average response time from 12 hours Alternate Hypothesis (HA3): The average response time is less than 12 hours. Question 4: Is the frequency of online card fraud more than that of offline card fraud? Null Hypothesis (H04): There is no significant difference in the frequency of online card fraud from offline card fraud. Alternate Hypothesis (HA4): There is significant difference in the frequency of online card fraud from offline card fraud. Question 5: Do any of the customers satisfaction scores of response time, the level of advice and the level of communication influence the overall satisfaction with the credit card fraud resolution team? Null Hypothesis (H05): The customers satisfaction scores of response time, the level of advice and the level of communication do not influence the overall satisfaction with the credit card fraud resolution team Alternate Hypothesis (HA5): The customers satisfaction scores of response time, the level of advice and the level of communication influence the overall satisfaction with the credit card fraud resolution team. Statistical Technique and Justification The hypothesis that has been stated above has to be tested using appropriate statistical techniques management. The techniques required to test the above stated hypothesis will be discussed here. To test the first hypothesis, two sample t-test will be used. A two sample t test or an independent sample t test is the most appropriate test that can be used to compare the difference of the means of the two different groups of a single variable (Traitler, Coleman Burbidge, 2017). To test the second hypothesis, analysis of variance (ANOVA) test will be used as this the most appropriate test to compare the means of more than two groups of a single variable (Wiley Pace, 2015). To test the third hypothesis, a one-sample t-test will be used as this is the most appropriate test to compare the mean of one variable with a pre determined mean of the variable (Chachi, Taheri Viertl, 2016). To test the fourth hypothesis, two sample t-test will be performed as this is the most appropriate test that can be used to compare the difference of the means of the two different groups of a single variable. To test the fifth hypothesis, regression analysis will be used as with the help of regression analysis only it is possible to find out whether there is any influence of the independent variables on the dependent variable (Draper Smith, 2014). It can be clearly observed that 34 percent of the respondents have not faced card fraud in the last 12 months. 66 percent of the respondents have experienced card fraud in the last 12 months. Thus, it can be said that most of the people around the world are now experiencing card fraud. The figures are given in table 5.1 and figure 5.1. Table 5.1: Number of people who faced card fraud in last 12 months Row Labels Count of Question1 1 278 2 142 Grand Total 420 Thus, as shown before, out of 420 respondents, 278 have experienced card fraud. Now, the difference between the numbers of card frauds experienced by these 278 people across gender has to be tested. At first, the difference between the numbers of offline card frauds has been tested. Table 5.2: Two-Sample t-test for difference in offline fraud Male Female Mean 4.40 4.24 Variance 23.44 23.64 Observations 126 152 Pooled Variance 23.55 Hypothesized Mean Difference 0 df 276 t Stat 0.262 P(T=t) one-tail 0.397 t Critical one-tail 1.650 P(T=t) two-tail 0.793 t Critical two-tail 1.969 Statistical Interpretation: From table 5.2, it is evident that t-calculated (0.262) is less than t-critical (1.969) and p-value is more than the significance level (5 percent level of significance), thus, we can accept the null hypothesis (H01) that there is no significant difference between the offline card fraud experienced by males and females (p-value 0.793) at 5 percent level of significance. The average number of times the females get card frauds offline does not differ much from the number of times the males get card fraud offline. Therefore, people should me much more careful so that nobody can fraud them. Table 5.3: Two-Sample t-test for difference in online fraud Male Female Mean 5.80 6.66 Variance 14.98 15.52 Observations 126 152 Pooled Variance 15.28 Hypothesized Mean Difference 0 df 276 t Stat -1.818 P(T=t) one-tail 0.035 t Critical one-tail 1.650 P(T=t) two-tail 0.070 t Critical two-tail 1.969 Statistical Interpretation: From table 5.3, it is evident that t-calculated (-1.818) is less than t-critical (1.969) and p-value is more than the significance level (5 percent level of significance), thus, we can accept the null hypothesis (H01) that there is no significant difference between the offline card fraud experienced by males and females (p-value 0.070) at 5 percent level of significance. The average number of times the females get card frauds online does not differ much from the number of times the males get card fraud offline. Therefore, people should me much more careful while accessing their cards online so that nobody can fraud them. Table 5.4: Summary Statistics for ANOVA on Offline Card Fraud Groups Count Sum Average Variance Less than 25 years 67 326 4.87 24.45 26-35 years 66 309 4.68 24.25 36-45 years 80 358 4.48 23.64 46-55 years 42 106 2.52 18.21 More than 55 years 23 100 4.35 24.15 Table 5.5: ANOVA Table on Offline Card Fraud Source of Variation SS df MS F P-value F crit Between Groups 166.021 4 41.505 1.788 0.131 2.405 Within Groups 6335.753 273 23.208 Total 6501.773 277 Statistical Interpretation: From table 5.5, it is evident that f-calculated (1.788) is less than t-critical (2.405) and p-value is more than the significance level (5 percent level of significance), thus, we can accept the null hypothesis (H02) that there is no significant difference between the offline card fraud experienced across different age groups (p-value 0.131) at 5 percent level of significance. Non-Statistical Interpretation: The average number of times the people of different age groups get offline card fraud has no significant difference. Thus, from here it can be said that people of all age groups has an equal chance of getting card fraud offline. Table 5.6: Summary Statistics for ANOVA on Online Card Fraud Groups Count Sum Average Variance Less than 25 years 67 417 6.22 16.02 26-35 years 66 463 7.02 12.66 36-45 years 80 516 6.45 15.74 46-55 years 42 206 4.90 16.04 More than 55 years 23 141 6.13 16.66 Table 5.7: ANOVA Table on Online Card Fraud Source of Variation SS df MS F P-value F crit Between Groups 118.112 4 29.528 1.943 0.104 2.405 Within Groups 4148.654 273 15.197 Total 4266.766 277 Statistical Interpretation: From table 5.7, it is evident that f-calculated (1.943) is less than t-critical (2.405) and p-value is more than the significance level (5 percent level of significance), thus, we can accept the null hypothesis (H02) that there is no significant difference between the online card fraud experienced across different age groups (p-value 0.104) at 5 percent level of significance. The average number of times the people of different age groups get online card fraud has no significant difference. Thus, from here it can be said that people of all age groups has an equal chance of getting card fraud online as well as offline. From table 5.8 given below, it can be seen clearly that the average time that can be lost by a customer suffering from online fraud is 13.65 hours. Table 5.8: Descriptive statistics for amount of time lost (in hours) in resolving the most recent incident of credit card fraud Mean 13.65 Standard Error 1.05 Median 1 Mode 1 Standard Deviation 17.562 Sample Variance 308.430 Kurtosis -0.991 Skewness 0.844 Range 50 Minimum 0 Maximum 50 Sum 3795 Count 278 The company Visa Inc. has set a time-period of 12 hours. To test whether there will be any significant improvement to the response time; the following test has been done. Table 5.9: One-Sample t-test for difference in service time from predefined mean Amount of time lost (in hours) in resolving the most recent incident of credit card fraud Mean 13.65 Variance 308.43 Observations 278 Hypothesized Mean Difference 12 df 277 t Stat 1.568 P(T=t) one-tail 0.059 t Critical one-tail 1.650 P(T=t) two-tail 0.118 t Critical two-tail 1.969 From Table 5.9, it is evident that t-calculated (1.568) is less than t-critical (1.650) and p-value is greater than the significance level (5% level of significance), thus, we can reject that alternate hypothesis (HA3) that the average service time in resolving the problem of online fraud is not less than 12 hours (p-value 0.059) at 5% level of significance. The average service time (13.65 hours) is not less than 12 hours (value obtained from forecasting model). Therefore, the average service time should be used while advertizing for the company. From table 5.10, it can be clearly understood that the average number of times an offline card fraud occurs is 4 and the average number of times an online card fraud occurs is 6. Table 5.10: Descriptive statistics measures for the frequency of online and offline card fraud Offline Card Fraud Online Card Fraud Mean 4 6 Standard Error 0.29 0.24 Median 0 6 Mode 0 1 Standard Deviation 4.845 3.925 Sample Variance 23.472 15.403 Kurtosis -1.896 -1.346 Skewness 0.292 -0.075 Range 10 12 Minimum 0 0 Maximum 10 12 Sum 1199 1743 Count 278 278 Table 5.11: Two-Sample t-test for difference in offline and online card fraud Offline Card Fraud Online Card Fraud Mean 4 6 Variance 23.47 15.40 Observations 278 278 Pooled Variance 19.44 Hypothesized Mean Difference 0 df 554 t Stat -5.233 P(T=t) one-tail 0.000 t Critical one-tail 1.648 P(T=t) two-tail 0.000 t Critical two-tail 1.964 From table 5.11, it is evident that t-calculated (-5.233) is greater than t-critical (1.648) and p-value is less than the significance level (5 percent level of significance), thus, we can reject the null hypothesis (H04) that there is no significant difference between the offline and online card fraud (p-value 0.070) at 5 percent level of significance. Non-Statistical Interpretation: The average number of times people get card frauds online is much more than the number of times the people get offline card fraud. Therefore, the company Visa Inc. must invest in the updated online security that will decrease the number of online card fraud while doing online transactions. The following analysis has been performed to test the influence of the customers satisfaction scores of response time, the level of advice, and the level of communication on the overall satisfaction with the credit card fraud resolution team Table 5.12: Regression Statistics Multiple R 0.80 R Square 0.65 Adjusted R Square 0.64 Standard Error 1.04 Observations 278 Table 5.13: ANOVA df SS MS F Significance F Regression 3 536.252 178.751 166.415 0.000 Residual 274 294.310 1.074 Total 277 830.561 Table 5.14: Regression Coefficients Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 1.725 0.233 7.387 0.000 1.265 2.184 Response Time 0.246 0.058 4.271 0.000 0.133 0.360 Level of Advice 0.152 0.122 1.251 0.212 -0.087 0.392 Level of Communication 0.244 0.123 1.985 0.048 0.002 0.487 Statistical Interpretation From table 5.14, it can be seen clearly that coefficients of the independent variables response time, level of advice and level of communication are not equal to zero. Thus, it can be said that the null hypothesis (H05) is rejected. The variables response time, level of advice and level of communication does influence the overall satisfaction with the credit card fraud resolution team. 65 percent of the overall satisfaction can be explained by the variables response time, level of advice and level of communication. The prediction equation can be given as follows: Overall satisfaction = 1.725 + (0.246 * Response Time) + (0.152 * Level of Advice) + (0.244 * Level of Communication) The average score of overall satisfaction can be predicted 65 percent correctly by the scores of response time, level of advice and the level of communication given by the customers. Since the correctness of the prediction is quite high, the company should try to improve these scores in order to maximize the overall satisfaction of the customers. From the analysis conducted above, it has been stated clearly that the average number of card frauds (online or offline) do not differ across gender. It has also been stated that the average number of online and offline card frauds do not differ across different age groups. The average time required by the company Visa Inc is more than 12 hours which is not the claim the company has made. It has also been observed that the frequency of online card fraud is much more than that of offline card fraud. Thus, the company should take suitable measures of increasing security to reduce the frequency of card fraud during online transactions. Further, it has also been observed from the analysis that the overall satisfaction of the customers is influenced by the response time, level of advice and the level of communication of the card fraud resolution team. Recommendations The company Visa Inc. should take rapid measures on the account of customer security to reduce the frequency of card fraud that is taking place currently at the time of online transactions. The company should also develop the response time, level of advice and the level of communication of the card fraud resolution team in order to increase the overall satisfaction of the customers. References Cacciattolo, M. (2015). Ethical considerations in research. InThe Praxis of English Language Teaching and Learning (PELT)(pp. 61-79). SensePublishers. Chachi, J., Taheri, S. M., Viertl, R. (2016). Testing statistical hypotheses based on fuzzy confidence intervals.Austrian Journal of Statistics,41(4), 267-286. Draper, N. R., Smith, H. (2014).Applied regression analysis. John Wiley Sons. Traitler, H., Coleman, B., Burbidge, A. (2017). Testing the hypotheses.Food Industry RD: A New Approach, 227-247. Wiley, J. F., Pace, L. A. (2015). Analysis of variance. InBeginning R(pp. 111-120). 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