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Example: Making an inference about m 1 – m 2
Example: Making an inference about m 1 – m 2

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S3.1 - Cengage

... This conceptual equation states that for any individual, the value of the response variable ( y) can be constructed by combining two components: 1. The mean, which is given by E(Y )  b0  b1x1  b2x2  p  bp1xp1, is the mean y for individuals who have the same specific set of x-values as this in ...
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... upon y. The discrepancies y - y* for each individual may depend upon a great variety of factors, these factors may be different from one individual to another, and they may vary with time for each individual. (Haavelmo op. cit., p. 50). And further that: ... the class of populations we are dealing w ...
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... reviewing the employee training programs of AFB banks. His staff randomly selected personnel files for 100 tellers in the Southeast Region, and determined that their mean training time was 25 hours and that the standard deviation was 5 hours. The 88% confidence interval for the population mean of tr ...
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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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