Question

Defective electronics: A team of designers was given the task of reducing the defect rate in the manufacture of a certain printed ole circuit board. The team decided to reconfigure the cooling system. A total of 985 boards were produced the week before the reconfiguration was implemented, and 260 of these were defective. A total of 842 boards were produced the week after reconfiguration, and 194 of these were defective. Part: 0/2 Part 1 of 2 (a) Construct a 99% confidence interval for the decrease in the defective rate after the reconfiguration. Use the TI-84 Plus calculator and round the answers to three decimal places. A 99% confidence interval for the decrease in the defective rate after the reconfiguration is <21-22<0.

1. The 99% confidence interval for the decrease in the defective rate after the reconfiguration is (-0.018, 0.086).

### How to find Confidence Intervals?

Let the random variable & parameters be;
x1 : Number of successes from group 1
x2 : Number of successes from group 2
p1: Proportion of successes in group 1
p2: Proportion of successes in group 2
n1 : number of trial in group 1
n2: number of trial in group 2
We are given;
x1 = 260
n1 =985
x2 = 194
n2 = 842
Thus;
p1 = 260/985
p1 =0.2640
p2 = 194/842
p2 = 0.2304
Constructing a (1 – α)100% confidence interval for proportion from the formula;
(p₁ – p₂) – z√[((p₁(1 – p₁)/n₁) + p₂(1 – p₂)/n₂)]
plugging in z = 2.576 and the values of p₁, p₂, n₁ and n₂, we have the confidence interval as;
(-0.0184631, 0.0855743)
Therefore the 99% confidence interval for the decrease in the defective rate after the reconfiguration is (-0.018, 0.086).