The Dow Jones Industrial Average Yearly Return I have obtained from the following table:
http://www.1stock1.com/1stock1_139.htm
We use the last column.
The U.S. GDP growth rate is below:
We use third column.
- Compute the average, standard deviation and the coefficient of variation of each of the variables. In addition, graph the values of the DJIA on the percentage grow rate of the GDP.
I use Minitab 16 statistical software to complete this question:
Descriptive Statistics: GDP per capita growth, %; Dow Jones Rate
Variable Mean StDev CoefVar
GDP per capita growth, % 1,755 1,994 113,65
Dow Jones Rate 9,67 15,24 157,63
- Compute a 95% confidence interval for the population mean of each variable.
One-Sample T: GDP per capita growth, %; Dow Jones Rate
Variable N Mean StDev SE Mean 95% CI
GDP per capita growth, % 31 1,755 1,994 0,358 (1,023; 2,486)
Dow Jones Rate 31 9,67 15,24 2,74 ( 4,08; 15,26)
- Test the hypothesis that GDP grows faster than the DJIA.
We have to test the hypothesis that the mean of GDP is higher than DJIA. This is one-tailed t-test for two samples.
Two-Sample T-Test and CI: GDP per capita growth, %; Dow Jones Rate
Two-sample T for GDP per capita growth, % vs Dow Jones Rate
N Mean StDev SE Mean
GDP per capita growth, % 31 1,75 1,99 0,36
Dow Jones Rate 31 9,7 15,2 2,7
Difference = mu (GDP per capita growth, %) - mu (Dow Jones Rate)
Estimate for difference: -7,91
95% lower bound for difference: -12,59
T-Test of difference = 0 (vs >): T-Value = -2,87 P-Value = 0,996 DF = 31
Since p-value is 0.996 we failed to reject the null hypothesis and we can’t say that we have enough evidence that GDP grows faster than the DJIA.
- Compute the correlation coefficient between both variables and test the significance of the relationship.
Correlations: GDP per capita growth, %; Dow Jones Rate
Pearson correlation of GDP per capita growth, % and Dow Jones Rate = 0,125
P-Value = 0,503
The correlation is very low and insufficient. However, this value is insignificant because of such big p-value.
- Write the short paper described above on your findings and lessons learned from the exercises.
Based on the data set we have found, we can’t say that the growth rate of GDP and DJIA are related in some way. The correlation is very low and insignificant and the results of the tests are negative.
Sources
Dodge, Y. (2006) The Oxford Dictionary of Statistical Terms, OUP. ISBN 0-19-920613-9
Lund Research Ltd. "Descriptive and Inferential Statistics". statistics.laerd.com. Retrieved 2014-03-23.
Moses, Lincoln E. (1986) Think and Explain with Statistics, Addison-Wesley, ISBN 978-0-201-15619-5 . pp. 1–3
Hays, William Lee, (1973) Statistics for the Social Sciences, Holt, Rinehart and Winston, p.xii, ISBN 978-0-03-077945-9
