Question

The Gallup survey company conducted a poll in May 2011. Researchers asked a random sample of about 1000 U.S. adults the following question: “From what you know or have read about raising the debt ceiling, would you want your member of Congress to vote in favor of, that is, for raising the debt ceiling, to vote against raising the debt ceiling, or do you not know enough about this issue to say?” Forty-eight percent of the adults who responded said that they would want their Congress member to vote against raising the debt ceiling. In July, 2011, the survey researchers asked a new random sample of about 1000 U.S. adults the same question. Forty-two percent of the adults who responded indicated that they would want their Congress member to vote against raising the debt ceiling. The margin of error for a 95% confidence level for the difference in the two proportions of adults who want their Congress member to vote against raising the debt ceiling was reported as 4.35%.

Let pm represent the true proportion of adults who want their Congress member to vote against raising the debt ceiling in May, 2011 and pj represent the true proportion of adults who want their Congress member to vote against raising the debt ceiling in July, 2011. Which of the following represents the accurate alternative hypothesis for testing to see if there is a difference between the two population proportions?

A. ​HA: pm − pj ≠ 0

B. ​HA: pm − pj = 0

C. ​HA: pm − pj ≤ 0

Answer 1

The accurate alternative hypothesis is

A) pm-pj 0

Note : The null hypothesis is the hypothesis of no difference , in null hypothesis we generally put the sign "=" or "" and "". The null hypothesis is the opposite of alternative hypothesis , which is the research question here .

The research question is there a difference between the two population proportions . Thus it is a non directional test . That is why we put sign . If the research question were one population proportion is more than the other , the alternative hypothesis would have taken the sign '>' or '<'.