The Customers Purchasing Behaviors - Example

Data analysis with Minitab Student’s name: Instructor: Institution: a) i) Gender Purchasing Records Purchasing Record Gender Gender as an attribute variable has its outcomes described in terms of its attributes or characteristics, which are allocated numerical codes. The variables entities are assigned codes that represent an outcome during data collection. In this case, gender is the attribute variable of the study, and consists of male and female. The variables that are grouped as measured variables have their outcomes determined through a process of measurement. These measurements can be of discrete or continuous form. Purchasing record is a measured variable and is of discrete form. The study is investigating the relationship between: “Purchasing Amount” and “Gender” (Coded as 1=Male, 0= Female) Descriptive Statistics: AMOUNT Variable GENDER N N* Mean StDev Minimum Q1 Median Q3 AMOUNT 0 304 0 15.316 6.498 4.210 10.550 13.980 20.000 1 277 0 15.776 7.395 4.630 10.355 13.380 20.875 Variable GENDER Maximum IQR AMOUNT 0 36.250 9.450 1 39.580 10.520 The mean of the purchases that are conducted by the male is 15.776, while those of their female the counterparts lie approximately at 15.316. This shows that the population means of the two variables are roughly equal, as the following equation indicates: µfemale  µmale. This analysis indicates that gender does not influence the customers’ purchasing behaviors because their mean are almost equal or extremely close to each other. ii) This study requires hypothesis which will aids in establishing if there is a relationship between quantity of compact disks purchased by customers, and gender of the purchasers. The null hypothesis of the study is as follows: H0: The quantities of compact disks purchased by customers do not vary across gender. H0: mFemale = mMale 'Amount’ is not subjective by ‘Gender' H1: mFemale ¹ mMale 'Amount’ is subjective by ‘Gender‘ The null hypothesis is adopted when the true mean of the explanatory and response variable are equal. If the true is equal and the null hypothesis should be adopted, and this is enough evidence that the two variables are not correlated. To establish if a relationship exists between gender and the amount of compact disks purchased we have to analyze the data using the decision rule, which utilizes the t-ratio’s distribution that splits the area into proportions resulting to a threshold value. It the value falls within the 0.25 interval, and then the null hypothesis is adopted implying a relationship between the two variables is non-existent. The outcome of the analysis was as the diagram below indicates: The graph above indicates that the true means of the two variables are equal, which implies that the null hypothesis of the study should be adopted. The study’s null hypothesis was as follows: Ho: The quantities of compact disks purchased by customers do not vary across gender. From the analysis we have established that there is no correlation between the two variables, and thus we conclude as follows: The study has established that the quantity of compact disks purchased by customers does not vary across gender. The gender is not in any way correlated to the amount of compact disks purchased. b) i) The study seeks to establish the relationship between “Gender” and “Amount” and the hypothesis is stated as follows: H0: mFemale = mMale 'Amount’ is not subjective by ‘Gender' H1: mFemale ¹ mMale 'Amount’ is subjective by ‘Gender‘ If the value falls between the ranges of tvalue then, there will be no relationship between the two variables and the null hypothesis should be adopted, otherwise alternative hypothesis should be adopted. Two-Sample T-Test and confidence interval for gender, and amount variables Two-sample T for AMOUNT GENDER N Mean StDev SE Mean 0 304 15.316 17.7 6.498 1 277 15.776 16.3 7.395 Difference = mµ (0) - mµ (1) Estimate for difference: 4.237 T-Test of difference = 0 (vs not =): T-Value = 2.93 P-Value = 0.000 DF = 244.75 The analysis above indicates that the estimated z value falls under the tvalue range. This concludes that the null hypothesis should be adopted because a relationship between the two variables does not exist. Conclusion The quantity of goods purchased by customers from the supermarket does not vary across gender. Thus, the null hypothesis should be adopted. ii) Conclusion During data analysis, there are four circumstances as illustrated above. The detection of the link or connection between explanatory and response variable is the starting point. The above data was mainly describing response variable that is measurable, which was the amount of compact disks purchased in a supermarket. The data analysis methodology is represented diagrammatically by the figure below: If the values of explanatory and response variable are equal or lie closely then the two entities are not related. Otherwise, the two values are correlated and lead to the adoption of the null hypothesis. If the response variable’s value is dependent on the level of the explanatory variable’s value, then the value of the response variable is influenced by attributer explanatory variable. Therefore, attribute explanatory variable and response variable are connected. Conversely; If, the mean value of the response variable is no dependent of the attribute explanatory variable’s level then, the attribute explanatory variable and responses variable are not connected. The common methodologies that are used in the data analysis include: Initial data analysis, further data analysis, and lastly the description of variables’ connection if they exist. When the mean values of the response and explanatory variable have been determined, they will be analyzed graphically to determine where thy lie. As the diagram below indicates, if the mean of the two entities of the measurable variable lie close together or they are equal then, they are assumed not to be related. The figure below demonstrates the case where the true mean of the measured variable’s attribute are not equal, or even lie closely to each other. When this is the case, the attributes are assumed to be related. The diagram shows how the will appear. Box plots can also be used to represent the above case as follows: When the values are equal and not related then they will appear as follows: If the values are not equal and hence related they will be represented as follows: After carrying out ANOVA of the variable’s means the tvalue will be used to assess whether a connection between the two variables exist. Usually the distribution is divided into intervals as follows: +2.5%, 95% and -2.5% and from the table is 1.96. If the tvalue is found to lie between the ranges of then, the null hypothesis should be adopted. The diagram below shows the distribution of t ratios. When the mean of the variables are not normally distributed, then the distribution of the f ratio will appear as below. Normally distributed values are checked from z table. Read More