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Statistics LibreTexts

6.E: Sampling Distributions (Exercises)

  • Page ID
    1108
  • These are homework exercises to accompany the Textmap created for "Introductory Statistics" by Shafer and Zhang.

    6.1: The Mean and Standard Deviation of the Sample Mean

    Basic

    Q6.1.1

    Random samples of size \(225\) are drawn from a population with mean \(100\) and standard deviation \(20\). Find the mean and standard deviation of the sample mean.

    Q6.1.2

    Random samples of size \(64\) are drawn from a population with mean \(32\) and standard deviation \(5\). Find the mean and standard deviation of the sample mean.

    Q6.1.3

    A population has mean \(75\) and standard deviation \(12\).

    1. Random samples of size \(121\) are taken. Find the mean and standard deviation of the sample mean.
    2. How would the answers to part (a) change if the size of the samples were \(400\) instead of \(121\)?

    Q6.1.4

    A population has mean \(5.75\) and standard deviation \(1.02\).

    1. Random samples of size \(81\) are taken. Find the mean and standard deviation of the sample mean.
    2. How would the answers to part (a) change if the size of the samples were \(25\) instead of \(81\)?

    Answers

    S6.1.1

    \(\mu _{\bar{X}}=100,\; \sigma _{\bar{X}}=1.33\)

    S6.1.3

    1. \(\mu _{\bar{X}}=75,\; \sigma _{\bar{X}}=1.09\)
    2. \(\mu _{\bar{X}}\) stays the same but