In many southern U. S. states, porch ceilings are painted a light blue color. Some people believe that the color tricks spiders, wasps and other insects into thinking that the ceiling is the sky and that this reduces the number of insects found on the porches.
Dixie wonders if this is really true and decides to investigate. She enlists the help of $35$ homeowners in South Carolina whose homes have porches. On each of these homes she paints half of the porch ceiling white and half of the porch ceiling light blue. Which half gets which color is determined by tossing a coin. She also places an insect trap on both sides of each porch.
After a period of two weeks, she counts the number of insects caught in each trap and determines the average number of insects caught near each color of paint. Her results are shown in the table below.
|Sample Mean||Sample Standard Deviation|
|Difference (Blue - White)||-1.3||7.1|
Assuming all conditions are satisfied, what is the $p$-value for a test to determine whether using light blue paint on porch ceilings will reduce the mean number of bugs on the porch?