Exercise 1: A One-Sample t-test, n=16 — Possible Solution
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GIVEN
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H0: mu = 50
n = 16, x-bar = 54, s = 10

STEP 1: THE STANDARD ERROR
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SE = s / sqrt(n) = 10 / sqrt(16) = 10 / 4 = 2.5

STEP 2: THE T-STATISTIC
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t = (x-bar - mu0) / SE = (54 - 50) / 2.5 = 4 / 2.5 = 1.6

STEP 3: DEGREES OF FREEDOM
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df = n - 1 = 16 - 1 = 15

STEP 4: THE DECISION
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Given critical value at two-tailed alpha=0.05, df=15: 2.131

|t| = 1.6, which is less than 2.131.

Per this chapter's own decision rule, we FAIL TO REJECT H0 - the
observed sample mean is not far enough from 50 (in units of standard
error, accounting for the extra t-distribution uncertainty from
estimating s) to conclude a real difference exists.

WHY THIS WORKS AS AN ANSWER
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Each quantity is computed in the sequence this chapter's own one-
sample t-test method uses - standard error using the sample s, then
the t-statistic, then degrees of freedom via n-1 - and the decision is
made by directly comparing the resulting |t| against the given
critical value.