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    Sample Size, Margin of Error, Confidence Level

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    Sample Size, Margin of Error, Confidence Level. See attached file for full problem description.

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    https://brainmass.com/statistics/confidence-interval/sample-size-margin-of-error-confidence-level-102028

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    1

    Confidence level= 98%
    or Significance level alpha (a) = 0.02
    No of tails= 2
    Z value corresponding to 0.02 significance level and 2 tails= 2.3263

    Answer: Zc= 2.3263

    2 Margin of error= 3-2.7= 0.3

    3 Sample size

    Standard deviation =s= 17
    confidence interval= 99%
    Z corresponding to 99% and two tailed test is 2.5758
    We have to ensure that Z* sx < 2
    or sx < =2/Z
    or sx < 0.776458 =2/2.5758
    But
    sx=standard error of mean=s/square root of n
    s= 17

    or n=(s^2)/(sx^2)= 480 =17^2/0.776458^2

    Answer: sample size = 480

    4
    Standard deviation =s= 3.6
    sample size=n= 10
    sx=standard error of mean=s/square root of n= 1.1384 = ( 3.6 /square root of 10)
    Significance level=alpha (a) = 0.1 =1-0.9
    No of tails= 2

    Since sample size= 10 < 30
    and we are estimating the population standard deviation from sample standard deviation
    we will use t distribution
    t at the 0.1 level of significance and 9 degrees of freedom (=n-1) and2 tailed test= 1.8331
    ...

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