Question

Researchers conducted a study to determine whether the majority of community college students plan to vote in the next presidential election. They surveyed 650 randomly selected community college students and found that 55% of them plan to vote.
1. Give the null and alternative hypotheses for this research question.
a. H0: p = 0.50 and Ha: p /= 0.50.
b. H0: p = 0.50 and Ha: p > 0.50.
c. H0: p = 0.55 and Ha: p /= 0.55.
d. H0: μ = 0.55 and Ha: μ > 0.55.

Answer 1

Answer:

Null Hypothesis, $H_0$ : p = 0.50

Alternate Hypothesis, $H_A$ : p > 0.50

Step-by-step explanation:

We are given that Researchers conducted a study to determine whether the majority of community college students plan to vote in the next presidential election.

They surveyed 650 randomly selected community college students and found that 55% of them plan to vote.

Let p = proportion of community college students who plan to vote in the next presidential election

So, Null Hypothesis, $H_0$ : p = 0.50

Alternate Hypothesis, $H_A$ : p > 0.50

Here, null hypothesis states that the proportion of community college students who plan to vote in the next presidential election is equal to 50% or 0.50.

On the other hand, alternate hypothesis states that the proportion of community college students who plan to vote in the next presidential election is greater than 50% or 0.50 which means there is majority.

Also, the test statistics that would be used here is One-sample z proportion statistics;

                       T.S.  =  $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$  ~ N(0,1)

where,  $\hat p$ = sample proportion of community college students who plan to vote in the next presidential election in a sample of 650 selected = 55%

            n = sample of students = 650

Therefore, the above hypothesis would be correct for testing.