Unformatted text preview: l of conﬁdence would accompany each of
the following intervals:
1
sample mean ± 1.645(SD)?
2
sample mean ± 1.96(SD) or 2(SD)?
3
sample mean ± 2.575(SD)?
Interpretation: Ex: In 95% of all samples, the true
population mean will be within 2 standard errors of the sample
mean. Conﬁdence Intervals and Hypothesis Testing for Population Hypothesis Testing for One Population Mean
Comparing Two Means for Two Independent Populations
Comparing Two Means for Two Dependent Populations Hypothesis Testing for Population Means Halfwidth and Sample Size Calculation σ
∗
¯
X ± zα /2 ∗ √n Conﬁdence Interval for µ :
σ
∗
Halfwidth: h = zα /2 ∗ √n Sample size: n = ∗
z α /2 ∗ σ
h 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 tdistribution for small sample size
When the sample size is small or when the population
standard deviation is unknown, use tdistribution instead
of zdistribution When n <30, the sampling distribution of the
sample mean y is
¯
σ
¯
y ∼ t (µ , √ )
n
The CI for the sample mean is CI = y ± tα /2 SE (¯)
¯∗
y
where 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 OneSample Test for Population Mean µ
when the population standard deviation σ is known When σ is known, use the z test
The Test statistic is:
z= ¯
x − µ0
√
σ/ n 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 Large sample size test for µ
unknown σ and large n When σ is unknown and n is large, use z test Test statistics:
z= ¯
x − µ0
√
S/ n where S is the standard deviation of the sample. Conﬁdence Intervals and Hypothesis Testing for Population Hypothesis Testing for One Population Mean
Comparing Two Means for Two Independent Populations
Comparing Two Means for Two Dependent Populations Hypothesis Testing for Population Means Small sample size test for µ
small n and no restriction on σ For the sample size n is small and th...
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 Spring '08
 Ioudina
 Normal Distribution, Standard Deviation, Hypothesis testing

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