A buyer for a manufacturing plant suspects that his primary supplier of raw materials is overcharging. In order to determine if his suspicion is correct, he contacts a second supplier and asks for the prices on various identical materials. He wants to compare these prices with those of his primary supplier. The data collected is presented in the table below, with some summary statistics presented (all of these might not be necessary to answer the problems which follow). The buyer -believes that the differences are normally distributed and will use this sample to perform an appropriate test at a level of significance of 0.01.
Primary Secondary
Material Supplier Supplier Difference
1 $55 $45 $10
2 $48 $47 $1
3 $31 $32 - $1
4 $83 $77 $6
5 $37 $37 $0
6 $55 $54 $1

Sum: $309 $292 $17
Sum of Squares: $17,573 $15,472 $139