Question

160 students who were majoring in either math or English were asked a test question, and the researcher recorded whether they answered the question correctly. The sample results are given below. At the 0.10 significance level, test the claim that response and major are independent. Round your answer to 3 decimal places.

	Correct	Incorrect
Math	27	53
English	43	37

a. p-value=0.470, evidence not support claim

b. p-value=0.011, evidence support claim

c. p-value=0.470, evidence support claim

d. p-value=0.530, evidence support claim

e. p-value=0.011, evidence not support claim

Answer 1

Sol;

Ho:response and major are independent

Ha:response and major are dependent

alpha=0.10

To get chi sq and p value in R

Rcode:

R1 = c(27,53)
R2 = c(43,37)

rows = 2
contingencytable = matrix(c(R1, R2),
nrow=rows,
byrow=TRUE)
colnames(contingencytable) = c("correct ", "incorrect")   
rownames(contingencytable) = c("math","english")
contingencytable
chisq.test(contingencytable,correct=FALSE)

Output:

contingencytable
correct incorrect
math 27 53
english 43 37
> chisq.test(contingencytable,correct=FALSE)

   Pearson's Chi-squared test

data: contingencytable
X-squared = 6.5016, df = 1, p-value = 0.01078

INTREPRETATION:

chi sq=6.5016

P =0.011

P<0.10

Reject null hypothesis

No suffcient evidence to support the claim

e. p-value=0.011, evidence not support claim