In a survey of 5000 registered voters who reside in California, 2739 were found to be republican. Construct a confidence estimate for the tr

Question

In a survey of 5000 registered voters who reside in California, 2739 were found to be republican. Construct a confidence estimate for the true percentage of republicans among registered voters in California. Use a confidence level of 99%.

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Calantha 3 years 2021-08-19T04:35:42+00:00 1 Answers 5 views 0

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  1. niczorrrr
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    2021-08-19T04:37:28+00:00
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    Answer and Step-by-step explanation:

    given:

    Sample size is: n =5000

    The sample proportion is: Ṗ = 2739 / 5000 = 54.78%

    And the critical value of z for 99% confidence interval is

                                                     Z = 2.58

    For a 99 % confidence interval we use formula:

                                                       Ṗ ± z√(Ṗ(1- Ṗ)/n)

    By putting the given values in this formula:

                                                         0.54 ± 2.58√(0.54(1-0.54)/5000)

                                                  = 0.54 ± 0.018

    This gives us upper confidence limit of

     0.54 + 0.018 =0.558 = 0.54%

    This gives us lower confidence limit of

    o.54 – 0.018 = 0.522 = 0.53%

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