Question

Many Americans were happy with the Supreme Court's decision to accept same-sex marriage. A poll was conducted showing that among the 415 randomly selected Republicans, 178 were satisfied with homosexual acceptance in the U.S and among 599 randomly selected Democrats, 359 were satisfied with homosexual acceptance. Are Republicans less satisfied with homosexual acceptance in the U.S. compared to Democrats?

Show all 5 steps. Including P-Value and Critical Value.

Answer 1

For Republicans:

n1 = 415

x1 = 178

p̂1 = x1/n1 = 0.4289

For Democrats :

n2 = 599

x2 = 359

p̂2 = x2/n2 = 0.5993

α = 0.05

Null and Alternative hypothesis:

Ho : p1 = p2

H1 : p1 < p2

Pooled proportion:

p̄ = (x1+x2)/(n1+n2) = (178+359)/(415+599) = 0.529585799

Test statistic:

z = (p̂1 - p̂2)/√ [p̄*(1-p̄)*(1/n1+1/n2)] = (0.4289 - 0.5993)/√[0.5296*0.4704*(1/415+1/599)] = -5.3459

Critical value :

Left tailed critical value, z crit = NORM.S.INV(0.05) = -1.645

Reject Ho if z < -1.645

p-value :

p-value = NORM.S.DIST(-5.3459, 1) = 0.0000

Decision:

p-value < α, Reject the null hypothesis

Conclusion:

There is enough evidence to conclude that Republicans are less satisfied with homosexual acceptance in the U.S. compared to Democrats.