You intend to estimate a population proportion with a confidence interval. The data suggests that the normal distribution is a reasonable ap

Question

You intend to estimate a population proportion with a confidence interval. The data suggests that the normal distribution is a reasonable approximation for the binomial distribution in this case. While it is an uncommon confidence level, find the critical value that corresponds to a confidence level of 97.1%.

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Ladonna 3 years 2021-08-19T08:14:30+00:00 1 Answers 0 views 0

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  1. RobertKer
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    2021-08-19T08:15:59+00:00
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    Answer:

    The critical value that corresponds to a confidence level of 97.1% is Z = 2.18.

    Step-by-step explanation:

    In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence level of 1-\alpha, we have the following confidence interval of proportions.

    \pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

    In which

    z is the z-score that has a p-value of 1 - \frac{\alpha}{2}.

    97.1% confidence level

    So \alpha = 0.029, z is the value of Z that has a p-value of 1 - \frac{0.029}{2} = 0.9855, so Z = 2.18.

    The critical value that corresponds to a confidence level of 97.1% is Z = 2.18.

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