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Unit 9: Testing a Claim
9.3A—Significance Test for a
Population Mean
Objectives 9.3A:
Perform a significance test
• Write hypotheses
• Check conditions
• Perform the mechanics
• Make a decision linked in
♥ We ASSUME that the null hypothesis is true
♥ We choose an alpha level
♥ This alpha level is the probability of
committing a type 1 error.
♥ A type 1 error is rejecting a null hypothesis
when the null is actually true
♥ If alpha = 5%, then 5% of the samples will
have results that will lead me to reject the
null even though it is true.
Example: Bolts!
A manufacturer of a special bolt requires
that this type of bolt have a mean shearing
strength in excess of 110 lb. To determine
if the manufacturer’s bolts meet the
required standards a sample of 35 bolts
was obtained and tested. The sample mean
was 112.7 lb and the sample standard
deviation was 9.62 lb. Use this information
to perform an appropriate hypothesis test
with a significance level of 0.05.
Example: The Gem Show!
A jeweler is planning on manufacturing gold charms.
His design calls for a particular piece to contain 0.08
ounces of gold. The jeweler would like to know if the
pieces that he makes contain (on the average) 0.08
ounces of gold. To test to see if the pieces contain 0.08
ounces of gold, he made a sample of 16 of these
particular pieces and obtained the following data.
0.0773 0.0779 0.0756 0.0792 0.0777 0.0713 0.0818
0.0802 0.0802 0.0785 0.0764 0.0806 0.0786 0.0776
0.0793 0.0755
Use a level of significance of 0.01 to perform an
appropriate hypothesis test.
Example: Water?
A blogger claims that US adults drink an
average of five 8-oz glasses of water each day.
You think it is less than the blogger claims
and take a random sample of 24 adults.
Assume that the graph of your sample data
shows a mound shape with no outliers. Your
sample mean is 4.204 glasses with standard
deviation of 1.170.
Example: Body Temperature
I don’t believe that human body temperature
really is 98.6°F. To test my theory, I take a
random of sample of 130 people and measure
their temperature. The sample mean is 98.25°F
and the standard deviation is 0.73°F.
Is there sufficient evidence to claim that human
body temperature is not 98.6°F?
Computer Output
One-Sample T
Test of mu = 98.6 vs not = 98.6
130 98.2500
StDev SE Mean
95% CI
0.7300 0.0640 (98.1233, 98.3767)