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9.6: Two Independent Samples Exercises

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    Exercise \(\PageIndex{1}\)

    Determine whether to reject or fail to reject the null hypothesis in the following situations:

    1. \(t(40) = 2.49\), p = 0.01
    2. \(\overline{X_{1}}=64, \overline{X_{2}}=54, n_{1}=14, n_{2}=12, s_{\overline{X_{1}}-\overline{X_{2}}}=9.75, p> 0.05\)
    1. Reject
    2. Fail to Reject

    Exercise \(\PageIndex{2}\)

    A researcher wants to know if there is a difference in how busy someone is based on whether that person identifies as an early bird or a night owl. The researcher gathers data from people in each group, coding the data so that higher scores represent higher levels of being busy.  Test for a difference between at the .05 level of significance by going through the four steps of Null Hypothesis Significance Testing with data provided in Table \(\PageIndex{1}\).

    Table \(\PageIndex{1}\)- Descriptive Statistics of Busyness for Two Groups
    Sample Mean SD N
    Night Owl 19.50 6.14 8
    Early Bird 26.67 3.39 9



    Step 1: 

    • Research Hypothesis:  Night owls score higher on the busyness survey than early birds.  [Your research hypothesis might be opposite, but Dr. MO is a night owl and feels like she is very busy...]
      • Symbols:  \( \bar{X_{NO}} >\bar{X_{EB}} \)
    • Null Hypothesis:  Night owls score similar on the busyness survey as early birds.
      • Symbols:   \( \bar{X_{NO}} = \bar{X_{EB}} \)

    Step 2: One-tailed test, \(df\) = 15, \(t_{Critical}\) = 1.753

    Step 3: \(t_{calculated}\) = -3.03

    Step 4: \(t_{critical} < |t_{calculated}|\), Reject the null hypothesis.

    Based on our data of early birds and night owls, we can conclude that early birds are busier (\(\overline{X_{EB}}=26.67\)) than night owls (\(\overline{X_{NO}}=19.50\)), \(t(15) = -3.03\), \(p < .05\). Although the means are statistically different, this does NOT support the research hypothesis because Dr. MO thought that Night Owls would be busier.

    Contributors and Attributions

    This page titled 9.6: Two Independent Samples Exercises is shared under a CC BY-NC-SA license and was authored, remixed, and/or curated by Michelle Oja.