Question

a student does a survey to see if the proportions of men and women who plan to get a degree in a health field are different. what kind of hypothesis test is this?
2 independent means t - test
1 mean t - test
2 means matched pairs t - test
2 proportions z - test
1 proportion z - test
which hypotheses do we want to test?
$h_0: p_1 = p_2$
$h_a: p_1
eq p_2$
$h_0: p_1
eq p_2$
$h_a: p_1 = p_2$
$h_0: p_1 = p_2$
$h_a: p_1 < p_2$
$h_0: p_1 = p_2$
$h_a: p_1 > p_2$

Explanation:

1. The student is comparing the proportions of two independent groups (men and women) regarding the likelihood of getting a health - field degree. So, a 2 Proportions z - test is appropriate as it is used to test the difference between two population proportions.
2. The null hypothesis ($H_0$) is typically a statement of no difference, so $H_0: p_1 = p_2$ where $p_1$ is the proportion of men and $p_2$ is the proportion of women. The alternative hypothesis ($H_A$) for a test to see if the proportions are different is $H_A: p_1

eq p_2$.

Answer:

1. 2 Proportions z - test
2. $H_0: p_1 = p_2$, $H_A: p_1

eq p_2$