Question

which hypotheses do we want to test?
h₀: p = 0.05
hₐ: p > 0.05
h₀: p = 0.05
hₐ: p ≠ 0.05
h₀: p ≠ 0.05
hₐ: p = 0.05
h₀: p = 0.05
hₐ: p < 0.05

Explanation:

In hypothesis testing, the null hypothesis (\(H_0\)) is a statement of no effect or a default assumption (usually an equality, like \(p = \text{some value}\)), and the alternative hypothesis (\(H_A\)) is what we suspect or want to test. The null hypothesis should be a statement of equality, so options with \(H_0: p
eq 0.05\) (third option) are invalid. The alternative hypothesis depends on the research question, but typically, the null is \(H_0: p = 0.05\) and the alternative is a two - tailed (\(p
eq0.05\)), left - tailed (\(p < 0.05\)) or right - tailed (\(p>0.05\)) test. However, the second option has \(H_0: p = 0.05\) (correct null) and \(H_A: p
eq0.05\) (a two - tailed alternative, which is a common form when we want to test if \(p\) is different from 0.05). The first option is right - tailed, the fourth is left - tailed, and the third has an incorrect null. So the correct pair is \(H_0: p = 0.05\) and \(H_A: p
eq0.05\).

Answer:

\(H_0: p = 0.05\)
\(H_A: p
eq0.05\) (the second option in the list)