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19 August, 08:31

Consider a large population with a mean of 150 and a standard deviation of 27. A random sample of size 36 is taken from this population. The standard error of the sampling distribution of sample mean; SE (X) = σx = q V ar (X) is equal to:

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  1. 19 August, 08:35
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    SE (X) = σx = 4.5

    Var (X) = 20.25

    Step-by-step explanation:

    Solution:-

    - A large population has a mean (u) and standard deviation (σ). The parameters of the population distribution are given as follows

    u = 150

    σ = 27

    - A sample of n = 36 people were taken from the population.

    - We will first estimate the sample standard deviation (σ) by assuming that the population is normally distributed with conditions:

    n ≥ 30

    u ≥ 10

    - The condition of normality are valid. The population is assumed to be normally distributed. The sample must also be normally distributed. The sample standard deviation (σx):

    σx = σ/√n = 27/√36

    σx = 4.5 ... sample standard deviation.

    - The sample variance can be determined by:

    Var (X) = (σx) ^2

    Var (X) = (4.5) ^2

    Var (X) = 20.25
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