Question

it is believed that the fraction of oil tankers that have spills each month is 0.18. an environmentalist, concerned about the way things are going, wants to find out the fraction of oil tankers that have spills each month. she believes the fraction is greater than 0.18.
what are the hypotheses for this test?

• $h_0: p \geq 0.18$ $h_a: p < 0.18$
• $h_0: p \geq 0.08$ $h_a: p < 0.08$
• $h_0: p = 0.18$ $h_a: p > 0.18$
• $h_0: p = 0.18$ $h_a: p \

eq 0.18$

Explanation:

To determine the hypotheses, we start with the null hypothesis (\(H_0\)) which is the statement of no effect or the status quo. Here, the original belief is that the fraction \(p = 0.18\), so \(H_0\) should be \(p = 0.18\) (or sometimes written as \(p\leq0.18\) or \(p\geq0.18\) but in the context of a one - tailed test for "greater than", the null is the opposite of the alternative). The alternative hypothesis (\(H_a\)) is what the environmentalist believes, that the fraction is greater than 0.18, so \(H_a:p > 0.18\). We check the options:

• The first option has \(H_0:p\geq0.18\) and \(H_a:p < 0.18\), which is a left - tailed test and not what we want.
• The second option has incorrect values (0.08 instead of 0.18).
• The third option has \(H_0:p = 0.18\) and \(H_a:p>0.18\), which matches our reasoning.
• The fourth option is a two - tailed test (\(H_a:p

eq0.18\)) and not what we want as the environmentalist is interested in if it's greater, not different in either direction.

Answer:

\(H_0:p = 0.18\) \(H_a:p>0.18\) (the third option among the given choices)