Question

Let α= .05. Astudy out of ETSU wants to test the claim that the proportion of students who consider themselves Democrats and the portion that consider themselves Republicans are equal. ETSU takes a SRS of size 1,003 and finds that 529 consider themselves Democrats. Using ρ0=.5 do we have evidence to conclude that there is a significant difference between political affiliation among students? Please right hypothesis, state conclusion and which test was used

Answer 1

H0: p = 0.5

Ha: p 0.5

We use normal distribution for proportion test.

Sample proportion = 529 / 1003 = 0.5274

Test statistics

z = - p / sqrt( p( 1 - p) / n)

= 0.5274 - 0.50 / sqrt( 0.50 * 0.50 / 1003)

= 1.74

p-value = 2 * P( Z > z)

= 2 * P (Z > 1.74)

= 2 * 0.0409

= 0.0818  

Since p-value > 0.05 level, we do not have sufficient evidence to reject H0 .

We conclude at 0.05 level that we fail to support the claim.