Unformatted text preview: population: The sample is no more than 10% of
the population
Independent Observations: all observations are
independent from one another Normal Population Assumption: real data are never
Normal
Nearly Normal Condition: The data come from a
distribution that is unimodal and symmetric. Independent Groups Assumption: The two groups
are independent from each other Independent groups: Students in two sections of Stat
401 taking a deparmentalConﬁdence IntervalsCompare the for Population
ﬁnal exam. and Hypothesis Testing Hypothesis Testing for Population Means Hypothesis Testing for One Population Mean
Comparing Two Means for Two Independent Populations
Comparing Two Means for Two Dependent Populations Sampling distribution of the sample diﬀerence
¯
¯
Y1 − Y2 2
2
Assuming Unequal Variances σ1 = σ2 Expectation:
¯
¯
E (Y1 − Y2 ) = µ1 − µ2
Standard deviation:
¯
¯
SE (Y1 − Y2 ) = 2
2
s1 s2
+
n1 n2 Sampling distribution of the sample diﬀerence is: 2
2
s1 s2 ¯
¯
Y1 − Y2 ∼ Normal µ1 − µ2 ,
+
n1 n2
Conﬁdence Intervals and Hypothesis Testing for Population Hypothesis Testing for Population Means Hypothesis Testing for One Population Mean
Comparing Two Means for Two Independent Populations
Comparing Two Means for Two Dependent Populations CI and Hypothesis Testing
2
2
Assuming Unequal Variances σ1 = σ2 Conﬁdence Interval:
2
2
s1 s2
+
n1 n2 ∗
¯
¯
Y1 − Y2 ± tdf Hypothesis Tests:
H0 : µ1 − µ2 = µ0 , Ha : µ1 − µ2 = µ0
H0 : µ1 − µ2 ≤ µ0 , Ha : µ1 − µ2 > µ0
H0 : µ1 − µ2 ≥ µ0 , Ha : µ1 − µ2 < µ0
Test Statistics:
∗
tdf = ¯
¯
Y1 − Y2 − µ0
2
s1
n1 s2 + n2
2 Conﬁdence Intervals and Hypothesis Testing for Population Hypothesis Testing for Population Means Hypothesis Testing for One Population Mean
Comparing Two Means for Two Independent Populations
Comparing Two Means for Two Dependent Populations Calculating the degrees of freedom degrees of freedom is the smaller of n1 − 1 or n2 − 1 Conﬁdence...
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 Spring '08
 Ioudina
 Normal Distribution, Standard Deviation, Hypothesis testing

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