Question

A polling company finds that 60% of Democrats give a ‘favorable’ rating for a senator and 52% of Republicans give a ‘favorable’ rating for the same senator. What should the company use if they want to know if this is a ‘statistically significant’ finding?

a. Independent two sample t-test

b. Two proportions z-test

c. One sample t-test

d. Matched pairs t-test

Answer 1

Two proportions z-test.

A z-test for two proportions is a hypothesis test that attempts to make a claim about the population proportions p₁ and p₂. Specifically, we are interested in assessing whether or not it is reasonable to claim that p₁ = p_2.

The Z-test for two proportions has two non-overlapping hypotheses, the null and the alternative hypothesis.

The null hypothesis is a statement about the population parameter which indicates no effect, and the alternative hypothesis is the complementary hypothesis to the null hypothesis.