Question

The categories of a categorical variable are given along with the observed counts from a sample. The expected counts from a null hypothesis are given in parentheses. Compute the χ2-test statistic, and use the χ2-distribution to find the p-value of the test.

Category	A	B	C	D
Observed    (Expected)	25(20)	35(40)	50(60)	90(80)

Round your answer for the chi-square statistic to two decimal places, and your answer for the p-value to four decimal places.

chi-square statistic = Enter your answer; chi-square statistic

p-value = Enter your answer; p-value

Answer 1

Using R code we can have the results.

CODE:

obs <- c(25,35,50,90)
exp <- c(20,40,60,80)
#Value of the statistic
sum(((obs-exp)^2)/exp)
#P-value
pchisq(sum(((obs-exp)^2)/exp),3,lower.tail = F)

OUTPUT:

> obs <- c(25,35,50,90)
> exp <- c(20,40,60,80)
> #Value of the statistic
> sum(((obs-exp)^2)/exp)
[1] 4.791667
> #P-value
> pchisq(sum(((obs-exp)^2)/exp),3,lower.tail = F)
[1] 0.1877036

Chi-squar statistic = 4.791667.

P-value = 0.1877036.