Question

Using R Studio (Include R Code)

A current Webster SGA polls show that for voters, 41.8% support Carol Davis, 39.2% support Josh Foster, and 19.0 % support Aaron Andrews. We conduct our own poll of 342 Walker School voters and get the following proportions: 43.1% Davis, 40.3% Foster, and 16.6% Andrews. Use the chi-squared hypothesis test to determine whether our survey is representative of typical Webster voters [point: if our survey is representative, the p-value should have us accept the Null hypothesis]

Answer 1

R code:

x=c(43.1,40.3,16.6)
p=c(41.8,39.2,19)
chisq.test(x, p)

Output:

Pearson's Chi-squared test

data: x and p
X-squared = 6, df = 4, p-value = 0.1991

Warning message:
In chisq.test(x, p) : Chi-squared approximation may be incorrect

Here we don’t trust the validity of the asymptotic approximation (see Warning message), the permutation approach is actually implemented in the chisq.test() function and safer to use here.

R code:

x=c(43.1,40.3,16.6)
p=c(41.8,39.2,19)
chisq.test(x, p,simulate.p.value = TRUE, B = 10000)

Output:

Pearson's Chi-squared test with simulated p-value (based on 10000
        replicates)

data: x and p
X-squared = 6, df = NA, p-value = 1

Since p-value>0.05 so we can conclude that our survey is representative of typical Webster voters.