Question

A politician claims 50% of the vote. A sample of 600 voters finds that 48% say they will vote
for the candidate. At the alpha=0.05 would you conclude the politician has less than 50%?

Can I have help with this problem?

Answer 1

Here, we have to use one sample z test for the population proportion.

The null and alternative hypotheses for this test are given as below:

H0: p = 0.50 versus Ha: p < 0.50

This is a lower tailed test.

We are given

Level of significance = α = 0.05

Test statistic formula for this test is given as below:

Z = (p̂ - p)/sqrt(pq/n)

Where, p̂ = Sample proportion, p is population proportion, q = 1 - p, and n is sample size

n = sample size = 600

p̂ = x/n = 0.48

p = 0.50

q = 1 - p = 0.50

Z = (p̂ - p)/sqrt(pq/n)

Z = (0.48 - 0.50)/sqrt(0.50*0.50/600)

Z = -0.9798

Test statistic = -0.9798

P-value = 0.1636

(by using z-table)

P-value > α = 0.05

So, we do not reject the null hypothesis

There is not sufficient evidence to conclude that the politician has less than 50% of the vote.