The Gallup Organization conducted a survey in which they ask

The Gallup Organization conducted a survey in which they asked 1020 adult Americans whether they felt low-income people paid their fair share of taxes. They asked whether they felt high-income people paid their fair share of taxes. For each income group, a success is identifiying an individual who feels the person pays his or her fair share of taxes. Is there significant difference in proportion of adult Americans who feel high-income people pay their fair share of taxes and the proportion who feel low-income people pay their fair share of taxes. Use a 0.05 level of signficance. What requirements must be met before testing?

Solution

Proportion of adult Americans who feel high-income people pay their fair share of taxes p1= (73+146)/1020 = 0.21
Proportion who feel low-income people pay their fair share of taxes p2 = (73+274)/1020 = 0.34

Pooled Sample Proportion p = (p1 * n1 + p2 * n2) / (n1 + n2)

= (0.21 * 1020 + 0.34 * 1020) / (1020 + 1020)
=0.275

Standard Error SE = sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2) ] }

= sqrt( 0.275 * ( 1 - 0.275 ) * ( (1/1020) + (1/1020) ))
= 0.02

Test Static z = (p1 - p2) / SE

= (0.21 -0.34)/0.02
= -6.5

P-value = 1 - (~0)
= ~1

P-value >0.05

Hence Failed to reject null hypothesis , there is insufficient evidence to say .