Based on the U.S. Demographic Information dataset provided, the income between the red states and blue states were compared. More specifically, independent samples t-test was conducted to compare the income between the two states. Independent samples t-test is a test that compares two independent groups of observation or measurements on a single characteristic (Rasmussen, 2007). Excel Data Analysis ToolPak was used to conduct the test. The results obtained are as shown below:
| t-Test: Two-Sample Assuming Equal Variances | ||
|
Variable 1 |
Variable 2 |
|
| Mean |
83,478.57 |
66,938.10 |
| Variance |
91,106,428.57 |
93,828,476.19 |
| Observations |
14.00 |
21.00 |
| Pooled Variance |
92,756,154.40 |
|
| Hypothesized Mean Difference |
0.00 |
|
| df |
33.00 |
|
| t Stat |
4.98 |
|
| P(T<=t) one-tail |
0.00001 |
|
| t Critical one-tail |
1.6924 |
|
| P(T<=t) two-tail |
0.00002 |
|
| t Critical two-tail |
2.0345 |
|
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To determine if there is a statistical difference between the two variables, we need to compare the p-value and the level of significance used (Cox, 2006). The P-value is 0.00002. The independent-sample t-test was conducted using an alpha value of 0.05 . According to Frost (n.d), if the p-value is less than the significance level, one can reject the null hypothesis and conclude that the effect is statistically significant. From the analysis, the p-value (0.00002) is much lower than the alpha value (0.05), i.e.
.
Hence, the difference between the income from red states and blue states is statistically significant at a significance level of 0.05. An independent sample t-test for the data provided was conducted using an alpha value of 0.1. The results obtained are as shown below. The difference between the income from red states and blue states is also statistically significant at a significance level of 0.1.
| t-Test: Two-Sample Assuming Equal Variances | ||
| Variable 1 | Variable 2 | |
| Mean |
83,478.57 |
66,938.10 |
| Variance |
91,106,428.57 |
93,828,476.19 |
| Observations |
14.00 |
21.00 |
| Pooled Variance |
92,756,154.40 |
|
| Hypothesized Mean Difference |
0 |
|
| df |
33 |
|
| t Stat |
4.9776 |
|
| P(T<=t) one-tail |
0.00001 |
|
| t Critical one-tail |
1.30774 |
|
| P(T<=t) two-tail |
0.00002 |
|
| t Critical two-tail |
1.6924 |
|
References
Cox, D. R. (2006). Principles of statistical inference . Cambridge university press.
Frost, J. (n.d). Significance level. [Online]. Retrieved April 23, 2020, from https://statisticsbyjim.com/glossary/significance-level/
Rasmussen, K. (2007). Encyclopedia of measurement and statistics (Vol. 1). Sage Publications, Inc.
