A researcher wants to use a paired sample to determine whether ...

[crobinson2013]

A researcher wants to use a paired sample to determine whether the mean number of hours spent exercising per week for married men differs from the mean number of hours spent exercising per week for married women.
 
  Identify the variable for the proposed hypothesis test.
  A) Gender
  B) Difference between mean hours of exercise per week for married men and mean hours of exercise per week for married women
  C) Marital status
  D) Hours of exercise per week

Question 2

For each of 200 randomly selected cities, Pete compared data for the number of churches in the city (x) and the number of homicides in the past decade (y).
 
  He calculated the linear correlation coefficient and was surprised to find a strong positive linear correlation for the two variables. Does this suggest that when a city builds new churches this will tend to cause an increase in the number of homicides? Why do you think that a strong positive linear correlation coefficient was obtained?

[adf223]

Answer to Question 1

D

Answer to Question 2

The positive linear correlation coefficient suggests that cities with a lot of churches also tend to have a high number of homicides. However, the fact that there is a correlation does not imply that there is causation. It is unlikely that building new churches would lead to an increase in the number of homicides. It is more likely that the correlation between the two variables is explained by their association with another variable (called a lurking variable), population. Larger cities tend to have both more churches and more homicides than small cities.