A statistician selected a random sample of 125 observations from a population with a known standard deviation equal to 16 and computed a sam

Question

A statistician selected a random sample of 125 observations from a population with a known standard deviation equal to 16 and computed a sample mean equal to 77. (SHOW WORK for CREDIT; round to 3 decimal places) a) Estimate the population mean with 93% confidence. b) Repeat Part a) using a 89% level of confidence. c) Repeat Part a) using a population variance equal to 441. d) Repeat Part a) using a sample size equal to 625. Any changes to C.I.?

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Arianna 2 months 2021-10-09T05:08:21+00:00 1 Answer 0 views 0

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    2021-10-09T05:09:25+00:00

    Answer:

    Step-by-step explanation:

    Given that a statistician selected a random sample of 125 observations from a population with a known standard deviation equal to 16 and computed a sample mean equal to 77

    We can use Z critical values since population std deviation is known. Also sample size >30

    We find std error of mean = \frac{16}{\sqrt{125} } \\=1.4311

    Margin of error = Z critical value * 1.4311

    Z critical values for 93% = 1.81

    for 89% = 1.60

    n Std error Z critical  Conf interval  

                89%    

         

    125 1.4311     1.6  (74.71024 79.28976
    )

         

         

              93%    

                1.81  (74.409709 79.590291
    )

    We find that when confidence level increases interval width increses.

    c) When sigma changes to 441, std error changes to \frac{16}{\sqrt{441} } \\=0.7619

    So we get

    n Std error Z critical  Conf interval  

               89%    

         

    441  0.7619     1.6  (75.781 78.219
    )

         

         

             93%    

               1.81  (75.621 78.37904)

    d) When n = 625, std error changes to 16/25 = 0.64

    n Std error Z critical  Conf interval  

            89%    

         

    441 0.64 1.6        (75.976 78.024
    )

         

         

           93%    

            1.81      (75.842 78.1584)

    When sample size increases, confidence interval width decreases.

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