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    Suppose that we want to estimate the mean score on a nationwide examination in finance, and for this purpose we choose a random sample of exam scores. The sample we choose has a mean of and a standard deviation of . For each of the following sampling scenarios, determine which test statistic is appropriate to use when making inference statements about the population mean.
    (In the table, refers to a variable having a standard normal distribution, and refers to a variable having a t distribution.)
    sampling scenario

    1. The same has size 13, and it is from a normally distributed population with unknown standard deviation.

    a. Z
    b. T
    c. Could use either Z or T
    d. Unclear

    2. The sample has size 80, and it is from a non-normally distributed population.

    a. Z
    b. T
    c. Could use either Z or T
    d. Unclear

    3. The sample has size 12, and it is from a normally distributed population with a known standard deviation of 75.

    a. Z
    b. T
    c. Could use either Z or T
    d. Unclear

    4. The sample has size 17, and it is from a population with a distribution about which we know very little.

    a. Z
    b. T
    c. Could use either Z or T
    d. Unclear
    5. The sample has size 90, and it is from a non-normally distributed population with a known standard deviation of 75.
    a. Z
    b. T
    c. Could use either Z or T
    d. Unclear

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    1. The same has size 13, and it is from a normally distributed population with unknown standard deviation.
    <br>
    <br>a. Z
    <br>b. T
    <br>c. Could use either Z or T
    <br>d. Unclear
    <br>
    <br>*sample size is small, but it is normally distributed, we can use T when the standard deviation is unknown.
    <br>
    <br>2. The sample has size 80, and it is from a non-normally distributed ...

    Solution Summary

    Suppose that we want to estimate the mean score on a nationwide examination in finance, and for this purpose we choose a random sample of exam scores. The sample we choose has a mean of and a standard deviation of . For each of the following sampling scenarios, determine which test statistic is appropriate to use when making inference statements about the population mean.
    (In the table, refers to a variable having a standard normal distribution, and refers to a variable having a t distribution.)
    sampling scenario

    1. The same has size 13, and it is from a normally distributed population with unknown standard deviation.

    a. Z
    b. T
    c. Could use either Z or T
    d. Unclear

    2. The sample has size 80, and it is from a non-normally distributed population.

    a. Z
    b. T
    c. Could use either Z or T
    d. Unclear

    3. The sample has size 12, and it is from a normally distributed population with a known standard deviation of 75.

    a. Z
    b. T
    c. Could use either Z or T
    d. Unclear

    4. The sample has size 17, and it is from a population with a distribution about which we know very little.

    a. Z
    b. T
    c. Could use either Z or T
    d. Unclear
    5. The sample has size 90, and it is from a non-normally distributed population with a known standard deviation of 75.
    a. Z
    b. T
    c. Could use either Z or T
    d. Unclear

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