# Math Help - Two sample test Hypothesis

1. ## Two sample test Hypothesis

When does this stuff get easier??

A random sample of 400 policies written on single persons revealed 120 had at least one accident in the previous three year period. Similarly, a sample of 600 policies written on married persons revealed that 150 had been in at least one accident. At the .05 significance level, is there a significant difference in the proportions of single and married persons having an accident during a three-year period?

2. This is clearer. It's a two sided test of a difference of binomial probabilities.

$H_0_s=p_m" alt="H_0_s=p_m" /> vs. $H_a_s\ne p_m" alt="H_a_s\ne p_m" />

Rejection region is $(-\infty, -1.96) \cup (1.96,\infty )$

Test stat is ${\hat p_s-\hat p_m\over \sqrt{ {\hat p_s\hat q_s\over n_s} +{\hat p_m\hat q_m\over n_m}}}$

Where $n_s=400$ and $\hat p_s={120\over 400}$.

Likewise $n_m=600$ and $\hat p_m={150\over 600}$.