Explore BrainMass

Explore BrainMass

    Known mean population and an unknown variance

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

    A normal population has a known mean 50 and unknown variance.

    a) A random sample of n=16 is selected from this population and the sample results are x-bar = 52 and s= 8. How unusual are these results? Explain.

    b) A random sample of n=30 is selected from this population and the sample results are x-bar = 52 and s=8. How unusual are these results. Explain.

    c) A random sample of n=100 is selected from this population and the sample results are x-bar = 52 and s=8. How unusual are these results? Explain

    d) Compare your answers to parts (a)-(c) and explain why they are the same or differ

    (Please see attached file).

    © BrainMass Inc. brainmass.com June 4, 2020, 12:40 am ad1c9bdddf
    https://brainmass.com/statistics/probability/known-mean-population-unknown-variance-352311

    Attachments

    Solution Preview

    Solution:

    (a) t = (x-bar - μ)/(s/√n) = (51.5 - 50)/(8/√16) = 0.75 and t = (52.5 - 50)/(8/√16) = 1.25
    P(x-bar = 52) = P(51.5 < x-bar < 52.5) = P(0.75 < t < 1.25) = 0.1172
    Probability that a sample has x-bar = 52 and s = 8 is 0.1172. This result is not unusual since 0.1172 is not a low probability.

    (b) t = (x-bar - μ)/(s/√n) = (51.5 - ...

    Solution Summary

    This solution provides all of the steps to solve the given statistics problems.

    $2.19

    ADVERTISEMENT