Hui conducts a correlational study on people's height and their vulnerability to anxiety. Her study establishes that no relationship exists between these two variables. This correlation is most likely represented by

 +.01

Explanation:

Correlation research is the research in which experiment is not performed for assessing and studying relationship between variables.No independent variable is altered at such research process.

According to the question, variables that do not form any relation with each other in correlation study is indicated through  +.01. Thus, Hui's research that consist variables as height of people and anxiety vulnerability that do not  have link with each other. This ,it will be represented through  +.01.  

the best and most correct answer among the choices provided by the question is the second choice "less supportive to the war of 1812"

the war of 1812 was a military conflict that lasted from june 1812 to february 1815, fought between the united states of america and the united kingdom, its north american colonies, and its native american allies.

i hope my answer has come to your . god bless and have a nice day ahead!