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9 December, 16:19

Consider a population variable measured in square-feet. The population standard deviation is 15 square-feet. How many observations do we need in our sample in order to be able estimate a 95% confidence interval with only 2.5 square-feet for error margin?

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  1. 9 December, 17:21
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    Given Information:

    standard deviation = σ = 15 ft²

    Confidence interval = 95%

    Margin of error = 2.5 ft²

    Required Information:

    Sample size = n = ?

    Answer:

    Sample size = n ≈ 139

    Step-by-step explanation:

    The required number of observations can be found using,

    Me = z (σ/√n)

    Where Me is the margin of error, z is the corresponding z-score of 95% confidence interval, σ is the standard deviation and n is the required sample size.

    Rearrange the above equation to find the required number of sample size

    √n = σz/Me

    n = (σz/Me) ²

    For 95% confidence level, z-score = 1.96

    n = (15*1.96/2.5) ²

    n = 138.29

    since the sample size can't be in fraction so,

    n ≈ 139

    Therefore, a sample size of 139 would be needed.
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