Question

Do students that are "Greek" (those who belong to a sorority/fraternity) have a tendency to be more involved in student government events than students who are "Not Greek"? Specifically, do more "Greek" students than "Not Greek" vote in the student elections? Let "Greek" students be group A and "Not-Greek" students be group B. Out of 250 randomly selected "Greek" students, 200 voted in the last election. Out of 500 randomly selected "Not Greek" students, 140 randomly selected "Not Greek" students voted in the last election. How would we write the alternative hypothesis? Group of answer choicesA. Ha: pA - pB = 0

B. Ha: pA - pB > 0
C. Ha: pA - pB < 0
D. Ha: pA - pB does not equal 0

Answer 1

Option B is correct.

The alternative hypothesis is given Mathematically as

Ha: pA - pB > 0

Explanation:

For hypothesis testing, the first thing to define is the null and alternative hypothesis.

The null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the directions of the test.

While, the alternative hypothesis takes the other side of the hypothesis; that there is indeed a significant difference between two proportions being compared. It usually confirms the the theory being tested by the experimental setup.

For this question, we want to test if students who are "Greek" (those who belong to a sorority/fraternity) have a tendency to be more involved in student government events than students who are "Not Greek" by checking the proportion of each group of students that turn out to vote in the student government elections.

If the proportion of Greek students that turn out to vote in the student government elections = pA

And

The proportion of non-Greek students that turn out to vote in the student government elections = pB

And the difference between them is given as

μ₀ = pA - pB

The theory to be tested that pA > pB, would constitute the alternative hypothesis and the null hypothesis would say that either the proportions are equal or proportion of non-greek students that turn out to vote is more than the proportion of Greek students that turn out to vote in the student government elections.

Mathematically,

The null hypothesis would be that

H₀: μ₀ = pA - pB ≤ 0

or

H₀: pA = pB

And the alternative hypothesis would be that

Hₐ: μ₀ = pA - pB > 0

or

Hₐ: pA > pB

Thereby, confirming the theory to be tested.

Hope this Helps!!!