Transcript CHAPTER EIGHT

Hypothesis Testing
with TWO Samples
Section 8.1
2 samples are independent if the sample
selected from one population is not related
to the sample selected from the 2nd
population.
2 samples are dependent if each member of
one sample corresponds to a member of
the other sample. (a.k.a. Paired or
Matched samples)
6.
Sample 1: the SAT scores of 44 high
school students.
Sample 2: the SAT scores of the same 44
high school students after taking an SAT
preparation course.
8.
Sample 1: the IQ scores of 60 females
Sample 2: The IQ scores of 60 males
3 ways the NULL hypothesis can be written:
µ1 = µ2
µ1 < µ2
µ1 > µ2
The samples must be randomly selected,
independent, and each sample size must
be at least 30
If n is not > 30, then each population must
have a normal distribution with σ
known.
1.
2.
3.
4.
5.
6.
7.
State the hypotheses
Specify level of significance, α
Determine the critical value(s)
Shade the rejection region(s)
Find the test statistic, z (new formula)
Make decision to reject or not reject H0
Interpret the decision in context
 18.
Claim: µ1 ≠ µ2 α = 0.05
Sample statistics:
mean1 = 52, s1 = 2.5, n1 = 70
mean2 = 45, s2 = 5.5, n2 = 60
 28.
A restaurant association says that
households in the US headed by people
under the age of 25 spend less on food
away from home than do households
headed by people ages 65-74. The mean
amount spent by 30 households headed by
people under the age of 25 is $1876 and
the standard deviation is $113. The mean
amount spent by 30 households headed by
people ages 65-74 is $1878 and the
standard deviation is $85. At α = 0.05, can
you support the restaurant association’s
claim?
Section 8.2
 10.
Claim: µ1 < µ2 α = 0.10
Sample statistics:
Mean1 = 0.345, s1 = 0.305, n1 = 11
Mean2 = 0.515, s2 = 0.215, n2 = 9
Assume σ21 = σ22
 12.
Claim: µ1 > µ2 α = 0.01
Sample statistics:
Mean1 = 52, s1 = 4.8, n1 = 16
Mean2 = 50, s2 = 1.2, n2 = 14
Assume σ21 ≠ σ22

14. The maximal oxygen consumption is a way
to measure the physical fitness of an
individual. It is the amount of oxygen in
milliliters a person uses per kilogram of body
weight per minute. A medical research center
claims that athletes have a greater mean
maximal oxygen consumption than nonathletes. The results for samples of the 2
groups are shown below. At α = 0.05, can you
support the center’s claim? Assume the
population variances are equal.
Athletes
NON Athletes
Mean1 = 56 ml/kg/min
Mean2 = 47 ml/kg/min
s1 = 4.9 ml/kg/min
s2 = 3.1 ml/kg/min
n1 = 23
n2 = 21