Automobile mechanics conduct diagnostic tests on 150 new cars of a particular make and model to determine the extent to which they are affec

Question

Automobile mechanics conduct diagnostic tests on 150 new cars of a particular make and model to determine the extent to which they are affected by a recent recall due to faulty catalytic converters. They find that 42 of the new cars tested do have faulty catalytic converters. The​ 99% confidence interval for the true proportion of new cars with faulty catalytic converters is​ _______.

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Amaya 4 weeks 2021-12-29T07:39:30+00:00 1 Answer 0 views 0

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    2021-12-29T07:41:17+00:00

    Answer:

    99% Confidence interval: (0.185,0.375)                                                  

    Step-by-step explanation:

    We are given the following in the question:

    Sample size, n = 150

    Number of cars that have faulty catalytic converters, x = 42

    \hat{p} = \dfrac{x}{n} = \dfrac{42}{150} = 0.28

    99% Confidence interval:

    \hat{p}\pm z_{stat}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}

    z_{critical}\text{ at}~\alpha_{0.01} = \pm 2.58

    Putting the values, we get:

    0.28\pm 2.58(\sqrt{\frac{0.28(1-0.28)}{150}}) = 0.28\pm 0.095\\\\=(0.185,0.375)

    The​ 99% confidence interval for the true proportion of new cars with faulty catalytic converters is​ (0.185,0.375)

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