Question

Suppose you work for a campaign to elect Candidate A.

Candidate A believes she will win the election.

Formally state the alternative hypothesis and null hypothesis.

A random poll is conducted and it is found that 525 out of 1000 voting citizens will vote for Candidate A.

Using an alpha level of .05, will you retain or reject the alternative hypotheses.

Answer 1

Solution:

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

H₀: p ≤ 0.5 versus H_a: p > 0.5

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

x = number of items of interest = 525

n = sample size = 1000

p̂ = x/n = 525/1000 = 0.525

p = 0.5

q = 1 - p = 0.5

Z = (p̂ - p)/sqrt(pq/n)

Z = (0.525 – 0.5)/sqrt(0.5*0.5/1000)

Z = 1.5811

Test statistic = 1.5811

P-value = 0.0569

(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 candidate A will win the election.