A team of designers was given the task of reducing the defect rate in the manufacture of a certain printed circuit board. The team decided to reconfigure the cooling system. A total of 973 boards were produced the week before the reconfiguration was implemented, and 254 of these were defective. A total of 847 boards were produced the week after reconfiguration, and 95 of these were defective.

a. Construct a 90% confidence interval for the decrease in the defective rate after the reconfiguration.

b. A quality control engineer claims that the reconfiguration has decreased the proportion of defective parts by more than 0.15. Does the confidence interval contradict this claim?