Is my statistical test significant or not?

    In NHST one computes the p value, the probability of getting results as or more surprising than what you got if you thought the relationship between two things was zero.  By what I think a rather silly convention, if that p value is .05 or less, one concludes that there is a relationship between the two things.  A good while back one of my able statistics teaching assistants called me from the lab and asked if it was OK if he jumped out of the window.  Since the lab was on the third floor, he clearly was distressed.  I asked him what was wrong.  He reminded of the trouble my students were having determining whether or not a statistical test was "significant" where "significant" means that p value is .05 or less.  I replied that that has bothered me for years and I have never been able to figure out why they have so much trouble with that.  He told me he had figured it out.  The students are unable to determine which of two numbers is smaller if the numbers are between 0 and 1.  Finding this hard to believe, I investigated.  Damn, he was right.  I embarked on an extensive program of arithmetic remediation focused on teaching students how to determine which of two numbers is smaller.  I had good success, but some never got it, as illustrated by the responses on the quiz item shown below.

 
 

Most often, p values that are less than or equal to .050 result in the declaration that the test of the null hypothesis is "statistically significant."  By this standard, which of the following p values would be considered statistically significant?
 
Correct Percent Answered
no
.470
 5%
no
.069
 5%
no
.051
 10%
yes
.049
 80%
.470, .069, and .051 are all greater than, not less than, .050.