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. Which of the following are the appropriate hypotheses in this case?a. H0: p = .19 vs. Ha: p < .19
b. H0: p = .19 vs. Ha: p > .19
c. H0: p < .25 vs. Ha: p = .25
d. H0: p = .25 vs. Ha: p < .25
e. H0: p = .25 vs. Ha: p not equal to .25

Answer 1

Answer:

d. H0: p = .25 vs. Ha: p < .25

Step-by-step explanation:

A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".  

The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".

The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".

On this case the claim that they want to test is: "If the proportion of 2005 has decreased from the info of 2004". So we want to check if the population proportion for 2005 is less than 0.25 (the value for 2004), so this needs to be on the alternative hypothesis and on the null hypothesis we need to have the complement of the alternative hypothesis.

Null hypothesis:$p \geq 0.25$

The null hypothesis can be on this way: $p=0.078$, but is better put the complement of the alternative hypothesis.    

Alternative hypothesis:[tex]p > 0.25/tex]

And the correct option would be:

d. H0: p = .25 vs. Ha: p < .25