Answer
a. We can reject $p_1=p_2$
b. It is possible that $p_1=p_2$.
c. We can reject $p_1=p_2$
d. They are not equal.
Work Step by Step
a. We use a ti-84 to find the confidence interval. To do this, we press “Stat” and then select “Tests.” Next, we select “2-PropZInt” to conduct the test. Doing this, we find that the confidence interval is $-.0798 \lt \mu_1-\mu_2\lt .149$. This does not go through 0, so we see that $p_1\ne p_2$.
b. We now use a similar method, except this time we consider $p_1$ and $p_2$ separately instead of $p_1-p_2$. Doing this, we see that the confidence intervals overlap. This would suggest that it actually is possible that $p_1=p_2$.
c. We now use a Ti-84 calculator. To solve, go to "Stat," then "Tests," and then select "Stats." Doing this, we find that the value of p is less than .05, so we see that $p_1\ne p_2$.
d. Since the results from part a and part c are the same, we see that $p_1$ and $p_2$ are not equal. Thus, we see that the method in part b involving overlap is the least effective method.
