Question

Sixty-five percent of registered voters, voted in the last presidential election. A researcher surveyed 1200 registered voters and found that 700 voted at the midterm elections. Can the researcher say that the proportion of the midterm election voters is different from the presidential elections at a 2% level of significance?

a) State the distribution you will use and why?

b) State the null and Alternate Hypothesis. Identify the claim.

c)Find the critical value.

d)find the test statistic and the P-Value

e) Make a decision. Write a conclusion.

Answer 1

Solution:

a) State the distribution you will use and why?

We will use z or normal distribution, because sampling distribution of proportion follows normal distribution. Here, we have to use z test for population proportion.

b) State the null and Alternate Hypothesis. Identify the claim.

H₀: p = 0.65 versus H_a: p ≠ 0.65

This is a two tailed test.

c)Find the critical value.

We are given level of significance = α = 0.02

Critical values = - 2.3263 and 2.3263

d)find the test statistic and the P-Value

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 = 700

n = sample size = 1200

p̂ = x/n = 700/1200 = 0.583333333

p = 0.65

q = 1 - p = 0.35

Z = (p̂ - p)/sqrt(pq/n)

Z = (0.583333333 – 0.65)/sqrt(0.65*0.35/1200)

Z = -4.8418

P-value = 0.0000

(by using z-table or excel)

e) Make a decision. Write a conclusion.

P-value < α = 0.02

So, we reject the null hypothesis

There is sufficient evidence to conclude that the midterm election voters are different from the presidential elections at a 2% level of significance?