Answer:
Option B is correct.
The alternative hypothesis is given Mathematically as
Ha: pA - pB > 0
Step-by-step 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!!!
can be converted into the power 
. Therefore we can rewrite the problem as 
and then follow the exponent rules about a power to a power, multiplying 1/2 and 3/4 together.
, which then can be turned into ![\sqrt[8]{10} ^{3x}](https://tex.z-dn.net/?f=%20%5Csqrt%5B8%5D%7B10%7D%20%5E%7B3x%7D)
, making the last option our answer.