In a study to estimate the proportion of residents in a city and its suburbs who favor the construction of a nuclear power plant, it was fou

Question

In a study to estimate the proportion of residents in a city and its suburbs who favor the construction of a nuclear power plant, it was found that 63 of 100 urban residents favor the construction, while only 59 of 125 suburban residents are in favor. If a 95% confidence interval was to be constructed for the difference of the proportions of urban and suburban residents who favor the construction of the plant, what would be the margin of error? Group of answer choices ± 0.0651 ± 0.1289 ± 0.0907 ± 0.1310

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Brielle 12 hours 2021-09-15T12:12:03+00:00 1 Answer 0

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    2021-09-15T12:14:00+00:00

    Answer:

    z_{\alpha/2}=1.96

    And the margin of error would be:

     ME = 1.96 \sqrt{\frac{0.63*(1-0.63)}{100} +\frac{0.472*(1-0.472)}{125}}= 0.1289

    And the best option would be:

    ± 0.1289

    Step-by-step explanation:

    We have the following info given from the problem

     X_1 =63 represent the number urban residents in favor the construction

    n_1 =100 represent the sample of urban residents

    \hat p_1= \frac{63}{100}=0.63 estimated proportion of urban residents in favor the construction

     X_2 =59 represent the number suburban residents in favor the construction

    n_2 =125 represent the sample of surban residents

    \hat p_2= \frac{59}{125}=0.472 estimated proportion of suburban residents in favor the construction

    And for this case the confidence interval for the difference in the two proportions is given by:

     (\hat p_1 -\hat p_2) \pm z_{\alpha/2} \sqrt{\frac{\hat p_1 (1-\hat p_1)}{n_1} +\frac{\hat p_2 (1-\hat p_2)}{n_2}}

    Since the confidence is 95% then the significance level is 5% and the critical value for this case using the normal standard distribution or excel is:

    z_{\alpha/2}=1.96

    And the margin of error would be:

     ME = 1.96 \sqrt{\frac{0.63*(1-0.63)}{100} +\frac{0.472*(1-0.472)}{125}}= 0.1289

    And the best option would be:

    ± 0.1289

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