Question

A survey of randomly selected registered voters asked if they considered themselves conservative or liberal and if they would be willing to pay higher taxes for gasoline as long as all of the additional revenue went to expanding public transportation. Of the 119 self-described conservatives surveyed, 95 responded that they were willing to pay the higher tax. Among the 131 self-described liberals surveyed, 112 responded that they were willing to pay the higher tax. Compute the test statistic for a hypothesis test to compare the population proportions of self-described conservatives and liberals that would be willing to pay the higher tax. Round your answer to two decimal places.

Answer 1

Solution :

Given that,

n₁ = 119

x₁ = 95

₁ = 0.7983

n₂ =131

x₂ = 112

₂ = 0.8550

Let be the pooled proportion.

= (x1 +x2)/(n1 + n2) = 0.828

1 - = 0.172

The test statistic z is

z =  

= (0.7983 - 0.8550)/[0.828*0.172*((1/119)+(1/131))]

= -1.19