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