Explore BrainMass

Explore BrainMass

    Probability of Proportions

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    A given population proportion is .25. For the given value of n, what is the probability of getting each of the following sample proportions?

    a. n = 110 and p̂ ≤ .21

    b. n = 33 and p̂ > .24

    c. n = 59 and .24 ≤ p̂ < .27

    d. n = 80 and p̂ < .30

    e. n = 800 and p̂ < .30

    © BrainMass Inc. brainmass.com March 5, 2021, 12:21 am ad1c9bdddf
    https://brainmass.com/statistics/sample-size-determination/probability-proportions-502074

    Attachments

    Solution Preview

    Please see the attachments.

    7.22. A given population proportion is .25. For the given value of n, what is the probability of getting each of the following sample proportions?
    Answers
    a. n = 110 and p̂ ≤ .21
    Here we can assume that p follows normal distribution with µ = 0.25 and standard deviation σ = = = 0.041286.
    We need P (p̂ ≤ .21). Standardizing p using and from standard normal tables, we have
    P (p̂ ≤ .21) = = P (Z < -0.96885) = 0.16631
    Details
    Normal Probabilities

    Common Data
    Mean 0.25
    Standard Deviation 0.041286

    Probability for X <=
    X Value 0.21
    Z Value -0.968851427
    P(X<=0.21) 0.166309662

    b. n = 33 and p̂ > .24
    Here we can assume that p follows normal distribution with µ = 0.25 and standard deviation σ = = = 0.075378.
    We need P (p̂ > .24). Standardizing p using and from standard normal tables, we have
    P (p̂ > .24) = = P (Z > -0.132665) = 0.5528
    Details
    Normal Probabilities

    Common Data
    Mean 0.25
    Standard Deviation 0.075378

    Probability for X >
    X Value 0.24
    Z Value -0.132664703
    P(X>0.24) 0.5528

    c. n = 59 and .24 ≤ p̂ < .27
    Here we can assume that p follows normal distribution with µ = 0.25 and standard deviation σ = = = 0.056373.
    We need P (.24 ≤ p̂ < .27). Standardizing p using and from standard normal tables, we have
    P (.24 ≤ p̂ < .27) =
    = P (-0.17739 < Z < 0.35478)
    = 0.2090
    Details
    Normal Probabilities

    Common Data
    Mean 0.25
    Standard Deviation 0.056373
    Probability for a Range
    From X Value 0.24
    To X Value 0.27
    Z Value for 0.24 -0.177389885
    Z Value for ...

    Solution Summary

    The probabilities of proportions are examined.

    $2.49

    ADVERTISEMENT