Assignment on Race and Income

Question: Write a report for how statistical analysis plays an important role in the estimation of the different types of data related to the business, industry and social sciences. Answer: Introduction Statistical analysis plays an important role in the estimation of the different types of data related to the business, industry and social sciences. Here, we want to analyse the data for the race and income of the persons. For checking the claim whether there is any difference in the average incomes for the two types of the race of the person, we need to use the inferential statistics or the testing of hypothesis. Also, we want to construct the confidence interval for the population proportion for the first type of the race of the person. By using the different statistical tools and techniques we can find out the confidence interval for the population proportion and by using the t test for the population mean we can check the claim regarding the significant difference in the average income for the persons of two types of races. The detail procedure is explained in the next topics. Methods For the purpose of constructing the confidence interval for the proportion for the first type of the race of the persons, we have to use the t confidence interval because we dont know the information about the population standard deviation. If we know the population standard deviation we use the z confidence interval for the population proportion. Also, we have to check the claim whether there is any significant difference in the income of the person with the two different types of the race. For checking this claim, we have to use the two sample t test for the population means. The statistical analysis is given as below: Statistical Analysis and Results First of all, we have to see the frequency distribution for the variable race. The frequency distribution for the race is given as below: Race Frequency Percent Valid Percent Cumulative Percent Valid 1.00 1312 86.8 86.8 86.8 2.00 159 10.5 10.5 97.4 3.00 40 2.6 2.6 100.0 Total 1511 100.0 100.0 The bar diagram for the variable race is given as below: From this bar diagram, it is observed that the persons with the race type of 1 are more in the given data set. Now, we have to find the 95% confidence interval for the population proportion for the type 1 race. The confidence interval is given as below: Confidence Interval Estimate for the Proportion Data Sample Size 1511 Number of Successes 1312 Confidence Level 95% Intermediate Calculations Sample Proportion 0.86829914 Z Value -1.9600 Standard Error of the Proportion 0.0087 Interval Half Width 0.0171 Confidence Interval Interval Lower Limit 0.8512 Interval Upper Limit 0.8853 The confidence interval for the proportion for the first type of the race of the person is given as (0.8512, 0.8853). Now, we have to check whether there is any significant difference in the average income for the race type of 1 and 2. For checking this claim we have to use the two sample t test for the population mean which is given as below: Group Statistics Race N Mean Std. Deviation Std. Error Mean Income 1.00 1312 137.9171 48.68959 1.34422 2.00 159 111.5811 51.15951 4.05721 t-test for Equality of Means T Df Sig. (2-tailed) Mean Difference Std. Error Difference 95% Confidence Interval of the Difference Lower Upper 6.406 1469 .000 26.33599 4.11143 18.27109 34.40089 6.162 194.309 .000 26.33599 4.27410 17.90641 34.76556 The p-value for this t test is given as 0.00 which is less than the given level of significance or alpha value 0.05, so we reject the null hypothesis that there is no any significant difference in the average income for the first and second type of race of the persons. This means, we concluded that there is a significant difference in the average income for the first and second type of the persons. Conclusions: It is observed that the persons with the race type of 1 are more in the given data set. The confidence interval for the proportion for the first type of the race of the person is given as (0.8512, 0.8853). We concluded that there is a significant difference in the average income for the first and second type of the persons. References: Schervish, Mark J. (1995). Theory of statistics (Corr. 2nd print. ed.). New York: Springer Moses, Lincoln E. (1986) Think and Explain with Statistics, Addison-Wesley Hays, William Lee, (1973) Statistics for the Social Sciences, Holt, Rinehart and Winston Rubin, Donald B.; Little, Roderick J. A., Statistical analysis with missing data, New York: Wiley 2002 Mosteller, F., Tukey, J. W. (1977). Data analysis and regression. Boston: Addison-Wesley. Mann, Prem S. (1995). Introductory Statistics (2nd ed.). Wiley. Babbie, Earl R. (2009). The Practice of Social Research (12th ed.). Wadsworth. Nick, Todd G. (2007). "Descriptive Statistics". Topics in Biostatistics.New York: Springer.