Transcript Slide 1

AP STATISTICS
LESSON 10 – 2
(DAY 3)
TESTS FOR A POPULATION MEAN
ESSENTIAL QUESTION:
How do the procedures for a
one sided and two sided test
differ?
Objective:
• To become more familiar with one-sided
and two-sided significance tests.
Inference toolbox
Significance tests
To test a claim about an unknown population parameter:
Step 1: Identify the population of interest and the
parameter you want to draw conclusions about state null
and alternative hypotheses in words and symbols.
Step 2: Choose the appropriate inference procedure.
Verify the conditions for using the selected procedure.
Step 3: If the conditions are met, carry out the inference
procedure.
• Calculate the test statistic.
• Find the P-value.
Step 4: Interpret your results in the context of the problem.
Z test for a Population Mean
To test the hypothesis Ho: μ = μ0 based on an SRS of size
n from a population with unknown mean μ and known
standard deviation σ, compute the one-sample z
statistic:
z = x – μ0
σ/√n
In terms of a variable Z having the standard normal
distribution, the P-value for a test of Ho against
Z test for a Population Mean
(continued…)
These P-values are exact if the population
distribution is normal and are approximately
correct for large n in other cases.
Example 10.13 Page 573
Executive Blood Pressures
• The national Center for Health Statistics reports that the
mean systolic blood pressure for males 35 to 44 years of
age is 128 and the standard deviation in this population
is 15.
• The medical director of a large company looks at the
medical records of 72 executives in this age group and
finds that the mean systolic blood pressure in this
sample is x = 126.07
• Is this evidence that the company’s executives have a
different mean blood pressure than the general
population?
• (Assume the executives have the same o = 15 as the
general population of adult males).
P-value for the Two Sided
Test