WFED540 Final Exam Task2 V.3
Ali Alkhalaf
December 8, 2015
## Source: local data frame [50 x 7]
##
## stateNames Population Income Illiteracy LifeExp Murder HSGrad
## (fctr) (int) (int) (dbl) (dbl) (dbl) (dbl)
## 1 Alabama 3615 3624 2.1 69.05 15.1 41.3
## 2 Alaska 365 6315 1.5 69.31 11.3 66.7
## 3 Arizona 2212 4530 1.8 70.55 7.8 58.1
## 4 Arkansas 2110 3378 1.9 70.66 10.1 39.9
## 5 California 21198 5114 1.1 71.71 10.3 62.6
## 6 Colorado 2541 4884 0.7 72.06 6.8 63.9
## 7 Connecticut 3100 5348 1.1 72.48 3.1 56.0
## 8 Delaware 579 4809 0.9 70.06 6.2 54.6
## 9 Florida 8277 4815 1.3 70.66 10.7 52.6
## 10 Georgia 4931 4091 2.0 68.54 13.9 40.6
## .. ... ... ... ... ... ... ...1. Compute and report correlations among these six variables and plot a correlogram representing these correlations.
## $r
## LifeExp Income HSGrad Population Illiteracy Murder
## LifeExp 1
## Income 0.34 1
## HSGrad 0.58 0.62 1
## Population -0.068 0.21 -0.098 1
## Illiteracy -0.59 -0.44 -0.66 0.11 1
## Murder -0.78 -0.23 -0.49 0.34 0.7 1
##
## $p
## LifeExp Income HSGrad Population Illiteracy Murder
## LifeExp 0
## Income 0.016 0
## HSGrad 9.2e-06 1.6e-06 0
## Population 0.64 0.15 0.5 0
## Illiteracy 7e-06 0.0015 2.2e-07 0.46 0
## Murder 2.3e-11 0.11 0.00032 0.015 1.3e-08 0
##
## $sym
## LifeExp Income HSGrad Population Illiteracy Murder
## LifeExp 1
## Income . 1
## HSGrad . , 1
## Population 1
## Illiteracy . . , 1
## Murder , . . , 1
## attr(,"legend")
## [1] 0 ' ' 0.3 '.' 0.6 ',' 0.8 '+' 0.9 '*' 0.95 'B' 1
2. Using ggvis, construct
a. plots that demonstrate the relationship between
i. HSGrad and Income,
and
ii. Illiteracy and Income.
b. A scatterplot of Murder by Illiteracy grouped by HSGrad.
3. Report tests of null hypotheses that
a. there is no difference in Income between states above median HSGrad and states less than or equal to median HSGrad,
## Source: local data frame [50 x 7]
##
## Population Income Illiteracy LifeExp Murder HSGrad median
## (int) (int) (dbl) (dbl) (dbl) (dbl) (dbl)
## 1 3615 3624 2.1 69.05 15.1 41.3 0
## 2 365 6315 1.5 69.31 11.3 66.7 1
## 3 2212 4530 1.8 70.55 7.8 58.1 1
## 4 2110 3378 1.9 70.66 10.1 39.9 0
## 5 21198 5114 1.1 71.71 10.3 62.6 1
## 6 2541 4884 0.7 72.06 6.8 63.9 1
## 7 3100 5348 1.1 72.48 3.1 56.0 1
## 8 579 4809 0.9 70.06 6.2 54.6 1
## 9 8277 4815 1.3 70.66 10.7 52.6 1
## 10 4931 4091 2.0 68.54 13.9 40.6 0
## .. ... ... ... ... ... ... ...##
## Welch Two Sample t-test
##
## data: StateIndicator2$Income by StateIndicator2$median
## t = -9.0052, df = 47.995, p-value = 6.973e-12
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -1179.5304 -748.9496
## sample estimates:
## mean in group 0 mean in group 1
## 3953.68 4917.92According to the t-test, the p-value= 6.973e-12 which is < α = .05, so reject the null hypotheses. So, there is statically difference in Income between states above median HSGrad and states less than or equal to median HSGrad, t = -9.0052, df = 47.995, p-value = 6.973e-12, 95% CI, [-1179.5304, -748.9496]
and
b. there is no difference in Murder between one group of states (to include Alabama, Alaska, Arkansas, Georgia, Illinois, Kentucky, Louisiana, Mississippi, and Michigan) and another group of states (Arizona, Connecticut, Iowa, Kansas, Maine, Minnesota, Nebraska, New Hampshire, North Dakota)
## Observations: 50
## Variables: 8
## $ Population (int) 3615, 365, 2212, 2110, 21198, 2541, 3100, 579,...
## $ Income (int) 3624, 6315, 4530, 3378, 5114, 4884, 5348, 4809...
## $ Illiteracy (dbl) 2.1, 1.5, 1.8, 1.9, 1.1, 0.7, 1.1, 0.9, 1.3, 2...
## $ LifeExp (dbl) 69.05, 69.31, 70.55, 70.66, 71.71, 72.06, 72.4...
## $ Murder (dbl) 15.1, 11.3, 7.8, 10.1, 10.3, 6.8, 3.1, 6.2, 10...
## $ HSGrad (dbl) 41.3, 66.7, 58.1, 39.9, 62.6, 63.9, 56.0, 54.6...
## $ median (dbl) 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1...
## $ StateIndicator3 (fctr) 1, 1, 0, 1, California, Colorado, 0, Delaware...## Source: local data frame [18 x 8]
##
## Population Income Illiteracy LifeExp Murder HSGrad median
## (int) (int) (dbl) (dbl) (dbl) (dbl) (dbl)
## 1 3615 3624 2.1 69.05 15.1 41.3 0
## 2 365 6315 1.5 69.31 11.3 66.7 1
## 3 2212 4530 1.8 70.55 7.8 58.1 1
## 4 2110 3378 1.9 70.66 10.1 39.9 0
## 5 3100 5348 1.1 72.48 3.1 56.0 1
## 6 4931 4091 2.0 68.54 13.9 40.6 0
## 7 11197 5107 0.9 70.14 10.3 52.6 1
## 8 2861 4628 0.5 72.56 2.3 59.0 1
## 9 2280 4669 0.6 72.58 4.5 59.9 1
## 10 3387 3712 1.6 70.10 10.6 38.5 0
## 11 3806 3545 2.8 68.76 13.2 42.2 0
## 12 1058 3694 0.7 70.39 2.7 54.7 0
## 13 9111 4751 0.9 70.63 11.1 52.8 1
## 14 3921 4675 0.6 72.96 2.3 57.6 1
## 15 2341 3098 2.4 68.09 12.5 41.0 0
## 16 1544 4508 0.6 72.60 2.9 59.3 0
## 17 812 4281 0.7 71.23 3.3 57.6 0
## 18 637 5087 0.8 72.78 1.4 50.3 1
## Variables not shown: StateIndicator3 (fctr)##
## Welch Two Sample t-test
##
## data: sub3$Murder by sub3$StateIndicator3
## t = -10.124, df = 15.943, p-value = 2.393e-08
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -10.454997 -6.833892
## sample estimates:
## mean in group 0 mean in group 1
## 3.366667 12.011111According to the t-test, the p-value = 2.393e-08 which is < α = .05, so reject the null hypotheses. So, there is a statically difference in Murder between the selected two groups of states, t = -10.124, df = 15.943, p-value = 2.393e-08, 95% CI, [-10.454997, -6.833892]