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Erikaprovido
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Tyro
Asked: 2021-04-11T15:04:12+00:00 In: ,

sampling distribution

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suppose a population consists of the scores of 5 teachers in a particular subject as follows 8, 9, 10, 11, and 12. by using a sampling distribution, estimate the population mean (u) using a random variable of size n=2

z score

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  2. acedstud

    The table below shows the possible samples of size 2 from the population.

    Draw 1/Draw 2 8 9 10 11 12
    8 8, 8   (8) 8, 9   (8.5) 8, 10   (9) 8, 11   (9.5) 8, 12   (10)
    9 9, 8   (8.5) 9, 9   (9) 9, 10   (9.5) 9, 11   (10) 9, 12   (10.5)
    10 10, 8   (9) 10, 9   (9.5) 10, 10   (10) 10, 11   (10.5) 10, 12   (11)
    11 11, 8   (9.5) 11, 9   (10) 11, 10   (10.5) 11, 11   (11) 11, 12   (11.5)
    12 12, 8   (10) 12, 9   (10.5) 12, 10   (11) 12, 11   (11.5) 12, 12   (12)

    The following table shows the distribution of the means of the samples of size 2.

    \bar{x} f f\bar{x}
    8 1 8
    8.5 2 17
    9 3 27
    9.5 4 38
    10 5 50
    10.5 4 42
    11 3 33
    11.5 2 23
    12 1 12
    \sum{f}=25 \sum{f\bar{x}}=250

    mean (\mu) = \dfrac{\sum{f\bar{x}}}{\sum{f}}=\dfrac{250}{25}=10.

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