9.6: Two Independent Samples Exercises
 Page ID
 18072
Exercise \(\PageIndex{1}\)
Determine whether to reject or fail to reject the null hypothesis in the following situations:
 \(t(40) = 2.49\), p = 0.01
 \(\overline{X_{1}}=64, \overline{X_{2}}=54, n_{1}=14, n_{2}=12, s_{\overline{X_{1}}\overline{X_{2}}}=9.75, p> 0.05\)
 Answer

 Reject
 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 \(\PageIndex{1}\).
Sample  Mean  SD  N 

Night Owl  19.50  6.14  8 
Early Bird  26.67  3.39  9 
 Answer

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: Onetailed 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.
 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...]
Contributors and Attributions
Foster et al. (University of MissouriSt. Louis, Rice University, & University of Houston, Downtown Campus)
