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S10.3 - Hypothesis Tests, Standard Deviation Unknown
Hypothesis Tests for a Population Mean, Population Standard Deviation Unknown
11
Mathematics
Graduate
11/10/2013

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Term
The difference between hypothesis testing where sigma is unknown rather than known
Definition
Must use t-distribution rather than the z-distribution
Term
1. Properties of the t-distribution
Definition
The t-distribution is different for different degrees of freedom
Term
2. Properties of the t-distribution
Definition
The t-distribution is centered at 0 and is symmetric about 0
Term
3. Properties of the t-distribution
Definition
The area under the curve is 1. The area on either side of 0 equals 1/2
Term
4. Properties of the t-distribution
Definition
As t increases/decreases without bound, the graph approaches but never equals 0
Term
5. Properties of the t-distribution
Definition
The area in the tails of the t-distribution is a little greater than the area in the tails of the standard normal distribution
Term
6. Properties of the t-distribution
Definition
As the sample size n increases, the density curve of t gets closer to the standard normal density curve
Term
2 requirements using classical and p-value approach
Definition
1. The sample is obtained using simple random sampling
2. The sample has no outliers and population is normally distributed or n >= 30
Term
Test statistic, sd unknown =
Definition
(xbar-mew0)/(s/n^0.5)
Term
If p-value < alpha then
Definition
Reject the null
Term
If p-value > alpha then
Definition
Fail to reject null
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