Question

Q.N. 8) Does amount of education play a role in the healthiness of an individual? The following data represent the level of health and the highest degree earned for a random sample of individuals from the General Social Survey. Does the evidence suggest that health and education are related?

Excellent Good Fair Poor

Less than High School 72 202 199 62

High School 465 877 358 108

Junior College 80 138 49 11

Bachelor 229 276 64 12

Graduate 130 147 32 2

Use R to solve and show R code

Answer 1

Solution:

We are given that following table:

	Excellent	Good	Fair	Poor	Total
Less than high school	72	202	199	62	535
High school	465	877	358	108	1808
Junior College	80	138	49	11	278
Bechelor	229	276	64	12	581
Graduatrs	130	147	32	2	311
Column Totals	976	1640	702	195	3513

We have to use R to test the if there is evidence to suggest that health and education are related.

Hypothesis for this test are:

H0: health and education are not related or are independent.

Vs

H1: health and education are related or are dependent.

We use following R code: Copy this code and paste it in R and Run.

> Input =("
+ Injection.area Excellent Good Fair Poor
+ Less_than_High_School 72 202 199 62
+ High_School 465 877 358 108
+ Junior_College 80 138 49 11
+ Bachelor 229 276 64 12
+ Graduate 130 147 32 2
+ ")
> Matriz = as.matrix(read.table(textConnection(Input),
+                    header=TRUE,
+                    row.names=1))
> Matriz
                      Excellent Good Fair Poor
Less_than_High_School        72 202 199   62
High_School                 465 877 358 108
Junior_College               80 138   49   11
Bachelor                    229 276   64   12
Graduate                    130 147   32    2
> chisq.test(Matriz,
+            correct=TRUE)

        Pearson's Chi-squared test

data: Matriz
X-squared = 285.061, df = 12, p-value < 2.2e-16

From the above R code output, we have Chi-square test statistic value = 285.061 and corresponding p-value = 2.2e-16 = 0.0000.

Decision Rule: Reject H0 if p-value < 0.05, otherwise we fail to reject H0.

( since level of significance is not given, we assume it is 0.05)

Since p-value = 0.0000 < 0.05 level of significance, we reject H0 and hence we conclude that there is evidence to suggest that health and education are related.