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- Solutions
P-value Guidelines:
Keep this in mind: The method for finding the p-value is based on the alternative hypothesis.
Minitab will provide the p-value but if doing by hand using Table A1 observe the following:
For Ha: p ≠ p
o
then p-value =
2P(Z ≥ |z|)
For Ha: p > p
o
then p-value = P( Z ≥ z)
For Ha: p < p
o
then p-value = P( Z ≤ z)
Activity 10.1
The present success rate in the treatment of a particular psychiatric disorder is 0.65 (65%).
A research group creates a new treatment for this disorder. Their null hypothesis is that the success rate
for the new treatment is 0.65 (no different from the standard).
The alternative hypothesis is that the
success rate is
better
than 0.65 for the new treatment.
a. Let
p
= true success rate of the new treatment. Using mathematical notation, write null and alternative
hypotheses about
p
.
H
0
: p = .65
versus Ha: p > .65.
b. A clinical trial is done in which 144 of 200 patients who use the new treatment are successfully treated.
What is the value of = success rate for the sample? How does it compare to 0.65 (the old standard)?
144/200 = .72.
Sample value is greater than .65.
c.
In Minitab use
Stat>Basic Stats>1 proportion
, click
Summarized Data
, enter 200 for number of trials
and 144 for Number of events. Click on
Options
, AND enter .65 where it says “Test proportion” AND
select the alternative hypothesis as “greater than” AND also click on “Use test and interval based on
normal distribution.”
What value is given for the test statistic Z in the output?
2.08

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