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Testing_for_Means 9.1-9.5

# 645sd 2 sample mean 196sd or 2sd 3 sample mean 2575sd

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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 Half-width and Sample Size Calculation σ ∗ ¯ X ± zα /2 ∗ √n Conﬁdence Interval for µ : σ ∗ Half-width: 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 t-distribution for small sample size When the sample size is small or when the population standard deviation is unknown, use t-distribution instead of z-distribution 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 One-Sample 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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