Question: The Manager of the Toledo Mudhens decides to see whether batting practice (think of this as the equivalent a week long series of professional development seminars) has any impact. Twenty Mudhens take batting practice; they are a randomly selected experimental group. Ten Mudhens, randomly selected, take no batting practice (control group). After 30 games, the figures shown in the accompanying table are available. What can you tell the manager about his experiment, statistically and managerially (i.e. practically)?
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Batting Practice Group
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No-Practice Group
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Mean
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.212
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.193
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Standard Deviation
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.026
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.047
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Sample Size (n)
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20
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10
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State your null and alternative hypotheses:
a) Using data from the question above, calculate your t-score - which involves first calculating the standard of error for the difference (Is this a paired or independent sample?; assume unequal variance.)
b. Estimate the p-value for your t-score (using the simplified formula for degrees of freedom k equal to n1+n2-2, where n are the sample sizes.) You may do this using the Excel function=tdist(t, d.f., 1 tail)
c. Is the difference of means statistically different from zero?
d. Is it practically different from zero?
In other words, what can you tell the manager about this experiment? Should s/he institute the new batting practice procedure?