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.

Answer 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).

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