Transcript Chapter 10 Testing Claims

10.1 Hypothesis Testing
Objective: set up null and alternate
hypotheses
Define each of the following.
 Population mean
 Sample
mean
 Population
 Sample
standard deviation
standard deviation
 Standard
error of the mean
Process
 A claim is made
 Evidence
is collected to test the claim
 Data
are analyzed to decide the validity of
the claim
 State
conclusions
Hypothesis
a statement or claim regarding a
characteristic of a population
Hypothesis testing
a procedure used to test claims regarding a
characteristic of a population – it can be
based on sample evidence and probability
Level of significance (α)
the probability of making a Type I error
Null hypothesis
(H0)
is a statement to be tested. It is assumed true until
evidence indicates otherwise.
Alternative hypothesis
(H1)
is a claim to be tested. We are trying to find
evidence for the alternative hypothesis.
Three ways to set up null and alternative hypotheses :
Two-tailed test
Left-tailed test
Right-tailed test
According to the Statistical Abstract of the United States, the
mean outstanding credit card debt per cardholder was $4277 in
2000. A consumer credit counselor believes that the mean is
now more than the 2000 amount.
The US Census Bureau reported that the mean annual salary in
2002 was $51,194 for an individual whose highest degree was a
bachelor's. A government economist believes that the mean is
different today.
In 1997, 39.4% of females had ordered merchandise or services by
phone in the last 12 months. A market research analyst
believes that the percentage has declined because of Internet
purchases.
Determine the null and alternative hypotheses.
State whether the test is two-tailed, righttailed, or left-tailed.
The Medco pharmaceutical company has just
developed a new antibiotic for children. Among
the competing antibiotics, 2% of children who
take the drug experience headaches as a side
effect. A researcher for the Food and Drug
Administration wishes to test the claim that the
percentage of children taking the new antibiotic
who experience headaches as a side effect is
more than 2%.
The Blue Book value of a used 3-year-old Chevy
Corvette is $37,000. Grand wishes to test
the claim that the mean price of a used 3year-old Chevy Corvette in the Miami area is
different from $37,000.
The standard deviation of the contents in a 64ounce bottle of detergent using an old filling
machine was known to be 0.23 ounce. The
company purchased a new filling machine
and wants to test the claim that the standard
deviation for the new filling machine is less
than 0.23 ounce.
There are four possible outcomes from
hypothesis testing.
H0 is TRUE
H1 is TRUE
Do not reject H0
Correct
Conclusion
Type II Error
Reject H0
Type I Error
Correct
Conclusion
α = P(Type I error)
rejecting the null hypothesis when it is true
β = P(Type II error)
not rejecting the null hypothesis when the
alternative is true
We choose significance levels depending on the
consequences of making a Type I error. If
severe, we set α = 0.01. If the consequences are
not as severe, a higher level can be chosen, such
as 0.05 or 0.10.
After analyzing the evidence, a decision is made to
reject or not reject the null hypothesis.
Suppose the sample evidence indicates that the
null hypothesis is rejected. State the conclusion.
There is sufficient evidence to support the claim.
Suppose the sample evidence indicates that the
null hypothesis is not rejected. State the
conclusion.
There is not sufficient evidence to support the
claim.
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