A manager of a small store wanted to discourage shoplifters by putting signs around the store that said, "Shoplifting is a crime!", while at the same time making sure the signs would not reduce the number of sales. To test the effect on sales, the signs were displayed every other Wednesday for 8 weeks, and the numbers of sales for those four Wednesdays were 83, 73, 81, and 79. The numbers of sales for the four alternate Wednesdays without the sign were 84, 90, 82, and 84.
What type of t test should be used to decide if there was a significantly lower number of purchases made while the signs were displayed?
Using the results provided, tell me if the results were significant (and why)?
With Sign: N = 4; df = 3; M = 79; S2 = 18.67
No Sign: N = 4; df = 3; M = 85; S2 = 12.00
Cutoff score (t needed) (df= 6, p < .05, one-tailed) = -1.943.
t = -2.17
So your answer has three parts: what type of t test should be used, are these results significant, and why?