Financial Statistics: Relationship Between Variables and Income Level
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Added on Â 2023/01/23
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This study explores the relationship between variables such as age, gender, and occupation and their impact on income level. The research uses descriptive statistics, confidence intervals, and hypothesis testing to analyze the data. The results show no significant difference in income between professionals and technicians/trade workers.
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Financial statistics Financial statistics Student name: Tutor name: 1|P a g e
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Financial statistics Executive summary This business study was conducted in order to find out the relationship between variables and how independent variables such as age, gender and occupation affected income level. The researchalsosoughttoanswervarioushypotheses.Forexample,wastheresignificant relationship between age group and amount of income? The method of data collection that was used in this study was through the use of questionnaire. Sampling was done through simple random sampling since it was easier and took less time. Some of the statistics computed were measures of central tendencies like mean and median. Measures of spread such as standard deviation and variance were determined. The results of this research were presented in tables and graphs. It was found that there were more female (33) than male (27). It was also found that there was no significant difference in mean total income between technician traders and professionals. 2|P a g e
Financial statistics TASK 2: DESCRIPTIVE STATISTICS gender FrequencyPercentValid PercentCumulative Percent Valid Male2745.045.045.0 Female3355.055.0100.0 Total60100.0100.0 Table 1 Table 1 gives the distribution of the respondents by gender. It can be observed that the females were 33 representing 55% while the males were 27 representing 45%. Figure 1 Figure 1 gives the distribution of the respondents by gender. It can be observed that the females were 33 representing 55% while the males were 27 representing 45%. The graph gives a visual representation of the results hence easy quick interpretation. 3|P a g e
Financial statistics Age range FrequencyPercentValid Percent Cumulative Percent Vali d Over 70 years58.38.38.3 65-69610.010.018.3 60-64610.010.028.3 55-5958.38.336.7 50-54610.010.046.7 45-491220.020.066.7 40-4435.05.071.7 35-3958.38.380.0 30-3446.76.786.7 25-2923.33.390.0 20-2458.38.398.3 Under 20 years 11.71.7100.0 Total60100.0100.0 Table 2 Table 2 is of distribution of the respondents by age group. It can be observed that majority of the respondents fell under the age of between 45 and 49 years. They were 12 representing 20%. There was only one person who was under 20 years constituting to 1.7%. The total number of those who participated in the survey was 60 in total. 4|P a g e
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Financial statistics Figure 2 The figure above is a graphical representation of the distribution of the respondents by age group. It can be observed from the bar graph that the majority of the respondents were from age 45 to 49 years. occupation Frequenc y PercentValid Percent Cumulative Percent Vali d Not specified1728.328.328.3 Managers35.05.033.3 Professionals46.76.740.0 Technicians and trades workers 58.38.348.3 Community and personal service workers 610.010.058.3 Clerical and administrative worker 610.010.068.3 Sales worker58.38.376.7 Machinery operator and610.010.086.7 5|P a g e
Financial statistics driver Laborers23.33.390.0 Consultant, apprentices610.010.0100.0 Total60100.0100.0 Table 3 The table above is of the distribution of the participants by their professions. There were 12 professions in total. The managers were 3, professionals were 4, technicians and traders were 5, community and personal service workers were 6, clerical and administrative workers were 6, sales workers were 5, machinery operators and drivers were 6, laborers were 2 while consultants were 6. Figure 3 The figure above is of the distribution of the participants by their professions. There were 12 professions in total. The managers were 3, professionals were 4, technicians and traders were 5, 6|P a g e
Financial statistics community and personal service workers were 6, clerical and administrative workers were 6, sales workers were 5, machinery operators and drivers were 6, laborers were 2 while consultants were 6. Lodgment method FrequencyPercentValid PercentCumulative Percent Valid Agent4880.080.080.0 Self1220.020.0100.0 Total60100.0100.0 Table 4 Table 4 gives the distribution of the respondents by lodgment method. It can be observed that the agents were 48 representing 80% while the self were 12 representing 20%. Figure 4 Figure 4 gives the distribution of the respondents by lodgment method. It can be observed that the agents were 48 representing 80% while the self were 12 representing 20%. 7|P a g e
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Financial statistics DESCRIPTIVE STATISTICS Statistics Total incomeWork related deductions Taxable income NValid604060 Missin g 0200 Mean50895.21671810.525047004.6833 Median42593.5000584.500038382.0000 Std. Deviation43377.582633329.6251241499.93931 Variance1881614674. 6 11086403.43 5 1722244962. 864 Minimum1.00117.001.00 Maximum193302.0014756.00193299.00 Table 5 Table 5 above is of the descriptive statistics of total income, work related deductions and taxable income. It can be observed that the mean taxable income was 47,004.68 dollars. The median taxable income was 38,382.00 dollars. The highest taxable income was 193299 dollars while the lowest taxable income was 1 dollar. The mean total income was 50895.21 dollars. The median total income was 42,593.5 dollars. The highest total income was 193302 dollars while the lowest total income was 1 dollar. The mean work related deduction was 1810.52 dollars. The median work related deduction was 584.5 dollars. The highest work related deduction was 14756 dollars while the lowest total income was 117 dollar. 8|P a g e
Financial statistics Graph of total income Figure 5 Graph of work related deductions Figure 6 9|P a g e
Financial statistics Graph of taxable income Figure 7 TASK 3: CONFIDENCE INTERVALS 95% confidence interval for total mean income Total income amount Mean56732.4375 Median47663.5 Standard Deviation 45538.6782 9 Sample Variance2073771220 Count48 Confidence Level (95.0%)13223.0538 Table 6 The table above shows the 95% confidence interval for the mean total income. It can be observed that the mean lies between 56,732.44 Â± 13,223.05 dollars. This means that we are 95% confident that the populations mean lies in the range 56,732.44 Â± 13,223.05. 10|P a g e
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Financial statistics 95% confidence interval mean work related deductions Work related deductions Mean1207.01666 7 Median281.5 Standard Deviation2840.61467 1 Sample Variance8069091.71 2 Count60 Confidence Level (95.0%) 733.808581 2 Table 7 The table above shows the 95% confidence interval for the mean work related deductions. It can be observed that the mean lies between 1,207.02 Â± 733.8 dollars. This means that we are 95% confident that the populations mean lies in the range 1,207.02 Â± 733.8. Population means Population total mean income for agents = $ 57,233 Population mean work related deductions = $ 1,195 Comparing the population means with the confidence interval computed, it can be concluded that the population mean is within the 95% confidence interval. TASK 4: HYPOTHESIS TESTING a.Test for the difference in means of total income between professionals and technicians and trade workers. H0:There is no significant difference in total income between professionals and technicians and trade workers. Versus H1:There is a significant difference in total income between professionals and technicians and trade workers. The level of significance is 0.05 11|P a g e
Financial statistics Independent sample t-test is appropriate in this case since we are comparing the means of two independent variables. Results table Independent Samples Test Levene's Test for Equality of Variances t-test for Equality of Means FSig.tdfSig. (2- tailed) Mean Difference Std. Error Difference 95% Confidence Interval of the Difference LowerUpper Total income Equal variances assumed .648.447-.5547.597- 13911.8500 0 25120.1383 0 - 73311.5382 3 45487.838 23 Equal variances not assumed -.5846.754.578- 13911.8500 0 23801.5705 9 - 70611.6479 9 42787.947 99 Table 8 Table 8 above shows the results of the independent sample t-test. Comparing the p-value and the level of significance, it can be observed that p-value computed (0.45) is greater than the level of significance (0.05). This leads to a decision of not rejecting the null hypothesis. The conclusion is that there is no significant difference in total income between professionals and technicians and trade workers. b.Test for the difference in means of total income between professionals and technicians and trade workers. H0:There is no significant difference in taxable income between male and females. Versus H1:There is a significant difference in taxable income between male and females. The level of significance is 0.05 Independent sample t-test is appropriate in this case since we are comparing the means of two independent variables. 12|P a g e
Financial statistics Results table Independent Samples Test Levene's Test for Equality of Variances t-test for Equality of Means FSig.tdfSig. (2- tailed) Mean Difference Std. Error Difference 95% Confidence Interval of the Difference LowerUpper Taxable income Equal variances assumed 3.724.0591.50358.13816011.0808110656.2550 1 - 5319.7311 6 37341.892 77 Equal variances not assumed 1.44543.698.15616011.0808111080.5970 3 - 6324.7500 2 38346.911 63 Table 9 Table 9 above shows the results of the independent sample t-test. Comparing the p-value and the level of significance, it can be observed that p-value computed (0.06) is greater than the level of significance (0.05). This leads to a decision of not rejecting the null hypothesis. The conclusion is that there is no significant difference in taxable income between male and females. TASK 5: CORRELATION AND REGRESSION Model Summary ModelRR SquareAdjusted R Square Std. Error of the Estimate 1.107a.011-.00641615.07104 a. Predictors: (Constant), age_range TABLE 10 The table above shows the results of simple linear regression between taxable income (dependent) and age range (independent). The coefficient of determination (-0.006) and 13|P a g e
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Financial statistics coefficient of correlation (0.011) indicate very low correlation between the variables. It can be concluded that the explanatory variable is only able to explain 1.1% of the variation that occurs in the response variable. ANOVAa ModelSum of SquaresdfMean SquareFSig. 1 Regression1167232830.84 3 11167232830.84 3 .674.415b Residual100445219978. 140 581731814137.55 4 Total101612452808. 983 59 a. Dependent Variable: taxable income b. Predictors: (Constant), age range TABLE 11 The table above shows the results of simple linear regression between taxable income (dependent) and age range (independent). It is an anova table. Since p-value computed (0.42) is greater than the level of significance (0.05), it can be concluded that the model is insignificant. That is, there is no linear relationship between the dependent and the independent variable. Coefficientsa ModelUnstandardized CoefficientsStandardized Coefficients tSig. BStd. ErrorBeta 1(Constant)40163.2559915.0384.051.000 Age range1460.8031779.359.107.821.415 a. Dependent Variable: taxable income TABLE 12 Below is the linear regression model Taxableincome=1460.8(agerange)+40,163.26 The model indicates that a unit increase in age range will cause 1460.8 unit changes in the level of taxable income. To add on, it also means that when age range is zero, the taxable income will always be 40,163.26 dollars. However, the coefficient of the age range is considered not significant (p-value = 0.415). 14|P a g e
Financial statistics Scatterplot of taxable income and age 024681012 $- $50,000.00 $100,000.00 $150,000.00 $200,000.00 $250,000.00 Taxable Income vs age age range taxable income Figure 8 The figure above shows a scatterplot between taxable income and age range. It can be observed that there is no linear pattern between the two variables hence no linear relationship. CONCLUSION After the data analysis and result findings, the study came up with various conclusions. The first one is that the taxable income in not affected by age of a person. It can also be concluded that gender does not affect the amount of taxable income of an individual. To add on, there is no significant difference in total income between professionals and technicians and trade workers. This is to say that whether you are a technician or a professional, your total income is independent of whether you belong to either. Total income and taxable income are not normally distributed. They are all skewed to the right. 15|P a g e