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S11.1 - Inference about Two Means, Dependent Samples
Inference about Two Means, Dependent Samples
19
Mathematics
Graduate
11/10/2013

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Term
A sampling method is independent when
Definition
The individuals selected for one sample do not dictate which individuals are to be in a second sample
Term
A sampling method is dependent when
Definition
The individuals selected for one sample are used to determine the individuals in the second sample
Term
Matched-pairs samples
Definition
Dependent samples
Term
3 assumptions for testing hypotheses regarding the difference of two means using a matched-pairs design
Definition
1. The sample is obtained using simple random sampling
2. The sample data are matched pairs
3. The differences are normally distributed with no outliers or the sample size n >= 30
Term
mewd
Definition
The population mean difference of matched-pairs data
Term
Two-tailed test, two dependent means
H0: mewd =
H1: mewd =
Definition
H0: mewd = 0
H1: mewd not=to 0
Term
Left-tailed test, two dependent means
H0:
H1:
Definition
H0: mewd = 0
H1: mewd < 0
Term
Right-tailed test, two dependent means
H0:
H1:
Definition
H0: mewd = 0
H1: mewd > 0
Term
Test statistic of two dependent means, t0 =
Definition
dbar/(sd/n^0.5)
where dbar = the mean of differenced data
sd = standard deviation of differenced data
Term
Two-tailed test, classical approach
If t0 > t(alpha/2), then
Definition
Reject the null
Term
Left-tailed test, classical approach
If t0 < -talpha, then
Definition
Reject the null
Term
Right-tailed test, classical approach
If t0 > talpha, then
Definition
Reject the null
Term
If p-value < alpha then
Definition
Reject the null
Term
If p-value > alpha then
Definition
Fail to reject null
Term
Robust
Definition
Minor departures from normality will not adversely affect the results of the test
Term
To determine outliers, we can use
Definition
Boxplots
Term
Confidence interval about a population mean =
Definition
Point estimate +/- margin of error
Term
Lower bound CI, matched-pairs data =
Definition
dbar - t(alpha/2) x sd/n^0.5
Term
Upper bound CI, matched-pairs data =
Definition
dbar + t(alpha/2) x sd/n^0.5
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