Question

In June 2005, a CBS News/NY Times poll asked a random sample of 1,111 U.S. adults the following question: "What do you think is the most important problem facing this country today?" Roughly 19% of those sampled answered "the war in Iraq" (while the rest answered economy/jobs, terrorism, healthcare, etc.).

Exactly a year prior to this poll, in June of 2004, it was estimated that roughly 1 out of every 4 U.S. adults believed (at that time) that the war in Iraq was the most important problem facing the country. We would like to test whether the 2005 poll provides significant evidence that the proportion of U.S. adults who believe that the war in Iraq is the most important problem facing the U.S. has decreased since the prior poll.

What are the appropriate hypotheses in this case?

Answer 1

The appropriate null hypothesis is
`H_0: p = 0.25`

The appropriate alternative hypothesis is
`H_1: p < 0.25`

Explanation:

Exactly a year prior to this poll, in June of 2004, it was estimated that roughly 1 out of every 4 U.S. adults believed (at that time) that the war in Iraq was the most important problem facing the country.

At the null hypothesis, we test if the proportion is still the same, that is, of
`(1)/(4) = 0.25`. So

`H_0: p = 0.25`

We would like to test whether the 2005 poll provides significant evidence that the proportion of U.S. adults who believe that the war in Iraq is the most important problem facing the U.S. has decreased since the prior poll.

Decreased, so at the alternative hypothesis, it is tested if the proportion is less than 0.25, that is:

`H_1: p < 0.25`