Production engineers at Sinotron believe that a modified layout on its assembly lines might increase average worker productivity (measured in the number of units produced per hour). However, before the engineers are ready to install the revised layout officially across the entire firm's production lines, they would like to study the modified line's effects on output. The following data represent the average hourly production output of 12 randomly sampled employees before and after the line was modified:
Employee :1 2 3 4 5 6 7 8 9 10 11 12
Before: 49, 45, 43, 44, 48, 42, 46, 46, 49, 42, 46, 44
After : 49, 46, 48, 50, 46, 50, 45, 46, 47, 51, 51, 49
Construct a 95% confidence interval and determine whether the modified (after) layout has increased average worker productivity. Assume that the differences between hourly production outputs are normally distributed.