- The document discusses hypothesis testing, including setting up null and alternative hypotheses, types of errors, and conclusions. - It provides examples of hypothesis tests on population means and proportions using the classical approach. This includes stating hypotheses, calculating test statistics, determining critical values, and making conclusions based on whether the test statistic falls in the critical region. - The examples test hypotheses about student income, SAT scores, migraine rates, and the proportion of female physicians.

1. Modular 15
Ch 10.1 to 10.2 Part I

2. Ch 10.1 The Language of Hypothesis Testing
Objective A : Set up a Hypothesis Testing
Objective B : Type I or Type II Error
Ch 10.2 Hypothesis Test for a Population Mean
Objective C : State conclusions for Hypothesis Tests
Objective A : Classical Approach

3. Ch 10.1 The Language of Hypothesis Testing
Objective A : Set up a Hypothesis Testing
Hypothesis testing is a procedure, based on a sample evidence and
probability, used to test statements regarding a characteristic of one
or more populations.
– The null hypothesis is a statement to be tested.0H
– The alternate hypothesis is a statement that we are trying
to find evidence to support.
1H

4. Example 1 : Set up and .
In the past, student average income was $6000 per year.
(a) An administrator believes the average income has increased.
(b) The percentage of passing a Math course was 50%. A Math
professor believes there is a decrease in the passing rate.
(No change)6000:0H
1H0H
(A right-tailed test)6000:1H
5.0:0 pH
(A left-tailed test)5.0:1 pH

5. Ch 10.1 The Language of Hypothesis Testing
Objective A : Set up a Hypothesis Testing
Objective B : Type I or Type II Error
Ch 10.2 Hypothesis Test for a Population Mean
Objective C : State conclusions for Hypothesis Tests
Objective A : Classical Approach

6. Objective B : Type I or Type II Error
Type I Error →
Type II Error →
Rejecting when is true.0H 0H
We use for the probability of making Type I error.
We use for the probability of making Type II error.
For this statistics class, we only control the Type I error.
)10.001.0(
is also called the level of significance.
Not rejecting when is true.0H 1H
Ch 10.1 The Language of Hypothesis Testing

7. Ch 10.1 The Language of Hypothesis Testing
Objective A : Set up a Hypothesis Testing
Objective B : Type I or Type II Error
Ch 10.2 Hypothesis Test for a Population Mean
Objective C : State conclusions for Hypothesis Tests
Objective A : Classical Approach

8. Objective C : State Conclusions for Hypothesis Tests
If is rejected, there is sufficient evidence to support the
statement in .
0H
1H
If is NOT rejected, there is NOT sufficient evidence to
support the statement in .
0H
1H
Section 10.1 The Language of Hypothesis Testing

9. Example 1 : In 2007, the mean SAT score on the reasoning test for all
students was 710. A teacher believes that, due to the
heavy use of multiple choice test questions, the mean
SAT reasoning test has decreased.
0H(a) Determine and .
A Type I error is made when the sample evidence leads the
teacher to believe is not true when in fact
is true.
710
1H
710:0H
710:1H
(b) Explain what it would mean to make a Type I error.
710

10. A Type II error is made when the sample evidence leads the
teacher to believe is true when in fact is less than
710.
710
710:0H
710:1H
(c) Explain what it would mean to make a Type II error.
(d) State the conclusion if the null hypothesis is rejected.
There is enough evidence to support the teacher’s claim that
the mean SAT reasoning test score has decreased.

11. Example 2 : The mean score on the SAT Math Reasoning exam is 516.
A test preparation company states that the mean score of
students who take its course is higher than 516.
(a) Determine the null and alternative hypotheses that would be
used to test the effectiveness of the marketing campaign.
There is not sufficient evidence to support the mean score
of the reasoning exam is higher than 516.
516:0H
516:1H
(b) If sample data indicate that the null hypothesis should not be
rejected, state the conclusion of the company.

12. If we tested this hypothesis at the = 0.01 level, what is the
probability of committing a Type I error?
(c) Suppose, in fact, that the mean score of students taking the
preparatory course is 522. Has a Type I or Type II error been made?
Type II error.
(d) If we wanted to decrease the probability of making a Type II error,
would we need to increase or decrease the level of significance?
If we increase , we decrease and vice versa.
Since is the probability of committing Type I error, it is 0.01.
Therefore, we need to increase the level of significance in order
to decrease the probability of Type II error.

13. Example 3 : According to the Centers for Disease Control, 15.2% of
adults experience migraine headaches. Stress is a major
contributor to the frequency and intensity of headaches.
A massage therapist feels that she has a technique that
can reduce the frequency and intensity of migraine
headaches.
(a) Determine the null and alternative hypotheses that would be
used to test the effectiveness of the massage therapist's techniques.
There is sufficient evidence to support the massage therapist’s
program that can reduce the percentage of migraine headache
from 15.2%.
152.0:0 pH
152.0:1 pH
(b) A sample of 500 American adults who participated in the massage
therapist's program results in data that indicate that the null
hypothesis should be rejected. Provide a statement that supports
the massage therapist's program.

14. Type I error.
(c) Suppose, in fact, that the percentage of patients in the program
who experience migraine headaches is 15.3%. Was a Type I or Type
II error committed?

15. Ch 10.1 The Language of Hypothesis Testing
Objective A : Set up a Hypothesis Testing
Objective B : Type I or Type II Error
Ch 10.2 Hypothesis Test for a Population Mean
Objective C : State conclusions for Hypothesis Tests
Objective A : Classical Approach

16. sample proportion, .
Ch 10.2 Hypothesis Tests for a Population Proportion
– Test for a Proportion
A hypothesis test involving a population proportion can be
considered as a binomial experiment. As we learned from Ch 8.2,
the best point estimate of , the population proportion, is a
Z
p
n
x
pˆ
Objective A : Classical Approach
There are two methods for testing hypothesis.
Method 1 : The Classical Approach

17. Method 2 : The – Value ApproachP
We are going to focus on the Classical Approach for today’s lecture.

18. Testing Hypotheses Regarding a Population Proportion, .
Use the following steps to perform a proportion – Test provided thatZ
p

20. Example 1: Use the Classical Approach to test the following hypotheses.
versus25.0:0 pH 25.0:1 pH
25.0:0 pH
25.0:1 pH
Step 1 :
1.0,96,400 xn
Step 2 :
Step 3 :
1.0
Sample : 96,400 xn
24.0
400
96
ˆ
n
x
p
n
pp
pp
z
)1(
ˆ
00
0
0
400
)25.01)(25.0(
25.024.0
400
)75.0)(25.0(
25.024.0
0z 46.0 * (test statistic)
(left-tailed test)

21. Use Table V to determine critical value for :1.0
*
From Table V
1003.0 0985.02.1
08.0
(Closer to
0.1)
46.00z28.1z
1.0
Recall :
Since – statistic, , is not within the critical region, , fail to
reject .
Z
25.0:1 pH (left-tailed test)
0H
0z z
There is not enough evidence to support .25.0:1 pH
Step 4 :
Step 5 :

22. Example 2: The percentage of physicians who are women is 27.9%. In a
survey of physicians employed by a large university health
system, 45 of 120 randomly selected physicians were
women. Use the Classical Approach to determine whether
there is sufficient evidence at the 0.05 level of significance
to conclude that the proportion of women physicians at the
university health system exceeds 27.9%?
279.0:0 pH
279.0:1 pH
Step 1 :
Step 2 : 05.0
(right-tailed test)

23. Use Table V to determine critical value for :
Step 3 : Sample : 45,120 xn
375.0
120
45
ˆ
n
x
p
n
pp
pp
z
)1(
ˆ
00
0
0
120
)279.01)(279.0(
279.0375.0
120
)721.0)(279.0(
279.0375.0
0z 34.2 * (test statistic)
05.0
05.0
279.0:1 pH (right-tailed test)

24. From Table V
9495.0 9505.06.1
04.0
Since – statistic, ,falls within the critical region, , reject .Z 0H0z z
*
34.20z
645.1z
05.095.005.01
05.0
045.0
95.0
There is sufficient evidence to support the claim that the proportion
of female physicians exceeds 27.9%.
Step 4 :
Step 5 :