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.

Answers

  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).
    Read more about Confidence Interval at; https://brainly.com/question/17097944
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