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Sample: 25 college-bound friends, 12 who do brain-training and
13 who do not.
Next, we need to make a prediction about how the populations
compare to each other, and include a null hypothesis that states the
opposite of our prediction. Here are our hypotheses:
Research Hypothesis (H 1 ): People who do brain-training will have
higher history quiz scores than those who don’t do brain-training
( µµ > µµ 2 ). In other words, we are making a directional hypothesis that
1
the Population of Interest’s mean will be greater than the Comparison
Population’s mean.
Null Hypothesis (H 0 ): People who do brain-training will have
the same (or lower) history quiz score as those who don’t do brain-
training ( µµ ≤ µµ 2 ). In other words, the Population of Interest’s mean
1
is either the same or lower than the Comparison Population’s mean.
Step 2: Build Comparison Distribution As before, our sampling
or comparison distribution should represent no effect or the null
hypothesis, which in this case is no difference between the brain-
training groups. Because we are interested in differences between
means of groups, our comparison distribution will be a t-shaped
Distribution of Differences Between Means.
Mean of the Distribution of Differences Between Means: To build our
comparison distribution, we first need the mean. We do not have
any direct information about the population, so we will rely on the
logic of hypothesis testing with the null hypothesis. Our comparison
distribution represents the null, and our null states that there is no
difference between the groups, which would make the typical or mean
difference 0.
Population Variance: Next, we need to find our comparison distri-
bution’s variance. However, we need some other information in order
to find that. First, we need to estimate the population’s variance (see
Figure 10.5). To do that, we will take the information we have from
our samples and combine it. Specifically we will use each sample’s
2
2
estimate of the population variance (S and S ) to create the pooled
1
2
estimate of population variance (S 2 Pooled ). To do that we first calculate
the samples’ estimated variances,
S 1 2 == SS 1 = 62.22 = 5.66
df 1 11

S 2 2 == SS 2 = 82.00 = 6.83
df 2 12

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