Question

political opinion survey shows that of 200 Republicans​ surveyed, 80 opposed the building of power plants using nuclear energy. Similar results for a sample of 300 Democrats showed that 150 opposed building nuclear power plants. At a​ 5% significance​ level, use these results to test whether there is a significant difference in the proportion of Republicans and Democrats opposed to building power plants. Show all steps of the appropriate hypothesis test.

Answer 1

Solution :

Given that,

n₁ = 200

x₁ = 80

₁ = 0.4

n₂ = 300

x₂ = 150

₂ = 0.5

Let be the pooled proportion.

= (x1 +x2)/(n1 + n2) = 0.46

1 - = 0.54

1)

Hypothesis are

H₀ : p₁ = p₂ vs H_a : p₁ p₂

2)

The test statistic z is

z =  

   = (0.4 - 0.5)/[0.46*0.54*((1/200)+(1/300))]

= -2.20

Test statistic z = -2.20

3)

Now , observe that ,there is    sign in H1. So , the test is TWO tailed.

p value = 2 * P(Z < -2.66)

= 2 * 0.0139 ....(use z table)

= 0.0278  

p value is 0.0278  

4)

p value is less than = 0.05

reject the null hypothesis.

5)

There is sufficient evidence to support the claim that there is a significant difference in the proportion of Republicans and Democrats opposed to building power plants.