Prompt

  1. In a previous lab we tested the following hypotheses, LaTeX: H_0

    H

    0
    : LaTeX: mu=4.73

    μ

    =

    4.73
    and LaTeX: H_a

    H

    a
    : <img src="https://4cd.instructure.com/equation_images/%255Cmu%253C4.73" alt="LaTeX: mu

    μ

    <

    4.73
    (where LaTeX: mu

    μ
    is the mean number of alcoholic drinks consumed by students at a liberal arts college).

    In a random sample of 75 students, the mean was 3.93 alcoholic drinks consumed in a week. Here is the StatCrunch output from the hypothesis test.
    LaTeX: mu

    μ

    : Mean of variable
    LaTeX: H_0

    H

    0
    :
    LaTeX: mu=4.73

    μ

    =

    4.73

    LaTeX: H_A

    H

    A
    : LaTeX: mune4.73

    μ

    ≠

    4.73

    Hypothesis test results
    VariableSample MeanStd. Err.DFT-StatP-value
    number of drinks per week3.93333330.4359243474-1.82753430.0717

    Using this context and the StatCrunch output, explain the meaning of each of the following.

    1. Std. Err (standard error)
    2. T-stat (T-score)
    3. P-value
  2. In a previous matched pairs lab we tested the following hypotheses, where LaTeX: mu

    μ
    is the mean of the differences in corn yield for a plot of land (regular seed minus kiln-dried): H0: µ = 0 and Ha: µ < 0. In a random sample of 11 seeds of each type, the mean of the differences in the sample was -33.7. Here is a StatCrunch print-out of the hypothesis test.

    Paired T hypothesis test:
    LaTeX: mu_D=mu_1-mu_2

    μ

    D

    =

    μ

    1

    −

    μ

    2

    : Mean of the difference between Regular seed and Kiln-dried seed
    LaTeX: H_0

    H

    0
    : LaTeX: mu_D=0

    μ

    D

    =

    0

    LaTeX: H_A

    H

    A
    : <img src="https://4cd.instructure.com/equation_images/%255Cmu_D%253C0" alt="LaTeX: mu_D

    μ

    D

    <

    0

    Hypothesis test results
    DifferenceMeanStd. Err.DFT-StatP-value
    Regular seed – Kiln-dried seed-33.72727319.95134610-1.69047610.0609

    Differences stored in column, Differences.

    Using this context and the StatCrunch output, explain the meaning of each of the following.

    1. Std. Err (standard error)
    2. T-stat (T-score)
    3. P-value.

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