# 9.6: Two Independent Samples Exercises


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.