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| To test hypotheses regarding population standard deviations, we use |
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Definition
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| 2 requirements for testing hypotheses regarding two population standard deviations |
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Definition
1. The samples are independent simple random variables
2. The populations from which the samples are drawn are normally distributed
*These testing procedures are not robust |
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Definition
| Variance for population i |
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Definition
| Sample variance for population i |
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Definition
| Sample size for population i |
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Definition
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| 1. Characteristics of the f-distribution |
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Definition
| The f-distribution is not symmetric; it is skewed right |
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| 2. Characteristics of the f-distribution |
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Definition
| The shape of the f-distribution depends on the degrees of freedom in the numerator and the denominator |
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| 3. Characteristics of the f-distribution |
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Definition
| The total are under the curve is 1 |
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| 4. Characteristics of the f-distribution |
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Definition
| The values of F are always greater than or equal to zero |
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| F-statistic is found by using |
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Definition
| Degrees of freedom in the numerator/degrees of freedom in denominator, then find the f-statistic in critical value table according to alpha and degrees of freedom |
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| 3 assumptions for test hypotheses regarding two population sd's |
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Definition
1. The samples are obtained using simple random sampling
2. The sample data are independent
3. The populations from which the samples are drawn are normally distributed
*Not robust |
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Term
Two-tailed test, two population sd's
H0:
H1: |
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Definition
H0: sigma1 = sigma2
H1: sigma1 not=to sigma2 |
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Left-tailed test, two population sd's
H0:
H1: |
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Definition
H0: sigma1 = sigma2
H1: sigma1 < sigma2 |
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Right-tailed test, two population sd's
H0:
H1: |
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Definition
H0: sigma1 = sigma2
H1: sigma1 > sigma2 |
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Two-tailed test, classical approach
If F0 > F(alpha/2),n1-1,n2-1, then |
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Definition
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Left-tailed test, classical approach
If F0 < F(1-alpha),n1-1,n2-1, then |
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Definition
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Right-tailed test, classical approach
If F0 > F(alpha),n1-1,n2-1, then |
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P-value approach
If p-value < alpha, then |
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P-value approach
If p-value > alpha, then |
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Definition
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