According to an AP-Ipsos poll (June 15, 2005), 42% of 1001 randomly selected adult Americans made plans in May 2005 based on a weather repor

Question

According to an AP-Ipsos poll (June 15, 2005), 42% of 1001 randomly selected adult Americans made plans in May 2005 based on a weather report that turned out to be wrong.

a. Construct and interpret a 99% confidence interval for the proportion of Americans who made plans in May 2005 based on an incorrect weather report.
b. Do you think it is reasonable to generalize this estimate to other months of the year

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Thiên Hương 4 years 2021-07-17T07:11:30+00:00 1 Answers 21 views 0

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  1. binhan
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    2021-07-17T07:13:21+00:00
    Reply

    Answer:

    a) The 99% confidence interval for the proportion of Americans who made plans in May 2005 based on an incorrect weather report is (0.3798,0.4602). This means that we are 99% sure that the true population proportion is in this interval.

    b) No, since May is a month with a wide range of possible weather.

    Step-by-step explanation:

    a)

    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 zscore that has a pvalue of 1 - \frac{\alpha}{2}.

    42% of 1001 randomly selected adult Americans made plans in May 2005 based on a weather report that turned out to be wrong.

    This means that p = 0.42, n = 1001

    99% confidence level

    So \alpha = 0.01, z is the value of Z that has a pvalue of 1 - \frac{0.01}{2} = 0.995, so Z = 2.575.

    The lower limit of this interval is:

    \pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.42 - 2.575\sqrt{\frac{0.42*0.58}{1001}} = 0.3798

    The upper limit of this interval is:

    \pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.42 + 2.575\sqrt{\frac{0.42*0.58}{1001}} = 0.4602

    The 99% confidence interval for the proportion of Americans who made plans in May 2005 based on an incorrect weather report is (0.3798,0.4602). This means that we are 99% sure that the true population proportion is in this interval.

    b. Do you think it is reasonable to generalize this estimate to other months of the year

    No, since May is a month with a vast number of possible outcomes, as it is in the spring, not being in the winter(cold) or summer(hot), which means that it can be both hot or cold, wet or dry,…

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