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test statistic (z-score in this case).
From our sample we see that of 400 patients, 68 patients experienced
side effects.
This is equivalent to 17% (or pˆ = 68
400 = 0.17). From the sample we are already seeing some evidence to
support the
alternative (0.17 < 0.20), but is this significant? ( Business
Statistics) Chapter 8 January 4, 2017 14 / 48 Hypothesis Testing for p
Hypothesis Testing for p Recall that the z-score for a single
proportion is
−p
Z = pˆSE
q
where SE = p(1−p)
n
Note that we are using the standard error for p in the denominator
since we are assuming H0 is true. ( Business Statistics) Chapter 8
January 4, 2017 15 / 48 Hypothesis Testing for p Hypothesis Testing
for p 0.17−0.20
0.02 0.3
0.1 Z = −1.5 0.2 Probability Z= 0.4 Using the information provided
in the problem, we obtain
q
SE = 0.2(1−0.2)
= 0.02
400 0.0 Once we obtain the test
statistics, the next step is to
calculate the p-value. −4 −2 0 2 4 Z < −1.5 Remember that the p-
value is
the probability of obtaining a
test statistic as extreme or more
extreme. In this example we are
looking for a Z = −1.5 or
smaller (i.e.
P[Z ≤ −1.5]).
P[Z ≤ −1.5] = 0.0668 ( Business Statistics) Chapter 8 January 4, 2017
16 / 48 Hypothesis Testing for p One-tailed or Two-tailed Before we