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Section 9.1 Confidence Intervals: The Basics Point Estimator and
Section 9.1 Confidence Intervals: The Basics Point Estimator and

... Recall from the reading, the “mystery mean µ,” was from a population with a Normal distribution and σ=20. We took a SRS of n=16 and calculated the sample mean= 240.79. ...
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... Inference for One Mean Summary of Video The z-procedures for computing confidence intervals or hypothesis testing work in cases where we know the population’s standard deviation. But that’s hardly ever the case in real life. For times when we don’t know the population standard deviation but still wa ...
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... those needed for the case when σ is unknown (t*).  z*, depends only on the level of confidence,  t* depend on both the level of confidence and on the sample size (for example: the t* used in a 95% confidence when n=10 is different from the t* used when n=40). ...
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... you would set =2 -3. If the 95% large sample confidence interval for  is computed as (-5,10), Are there significant differences between those two tests according to the confidence interval? (a) Yes (b) No because no differences if =0 which falls in between the limits of the confidence interval ...
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... d. The population variance of highway 1 is different than the population variance of highway 2. e. None of the above. ...
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Inference - 國立臺灣大學 數學系

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Confidence Interval Estimation for a Population Mean

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Chapter 7 Estimation and testing

... distribution are given in Table 10 ; thus tν (0.25) is the 75th percentile or upper quartile whose value for different ν is given by the third column of figures in the main body of Table 10. These percentiles will be used extensively in the next section for statistical inference on Normal population ...
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3. The Sample Variance

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Chapter 4: Variability

< 1 ... 35 36 37 38 39 40 41 42 43 ... 114 >

Degrees of freedom (statistics)

In statistics, the number of degrees of freedom is the number of values in the final calculation of a statistic that are free to vary.The number of independent ways by which a dynamic system can move, without violating any constraint imposed on it, is called number of degrees of freedom. In other words, the number of degrees of freedom can be defined as the minimum number of independent coordinates that can specify the position of the system completely.Estimates of statistical parameters can be based upon different amounts of information or data. The number of independent pieces of information that go into the estimate of a parameter are called the degrees of freedom. In general, the degrees of freedom of an estimate of a parameter are equal to the number of independent scores that go into the estimate minus the number of parameters used as intermediate steps in the estimation of the parameter itself (i.e. the sample variance has N-1 degrees of freedom, since it is computed from N random scores minus the only 1 parameter estimated as intermediate step, which is the sample mean).Mathematically, degrees of freedom is the number of dimensions of the domain of a random vector, or essentially the number of ""free"" components (how many components need to be known before the vector is fully determined).The term is most often used in the context of linear models (linear regression, analysis of variance), where certain random vectors are constrained to lie in linear subspaces, and the number of degrees of freedom is the dimension of the subspace. The degrees of freedom are also commonly associated with the squared lengths (or ""sum of squares"" of the coordinates) of such vectors, and the parameters of chi-squared and other distributions that arise in associated statistical testing problems.While introductory textbooks may introduce degrees of freedom as distribution parameters or through hypothesis testing, it is the underlying geometry that defines degrees of freedom, and is critical to a proper understanding of the concept. Walker (1940) has stated this succinctly as ""the number of observations minus the number of necessary relations among these observations.""
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