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- https://biz.libretexts.org/Workbench/MGT_235/10%3A_Linear_Regression_and_Correlation/10.07%3A_Predicting_with_a_Regression_EquationThe Gauss-Markov theorem assures us that the point estimate of the impact on the dependent variable derived by putting in the equation the hypothetical values of the independent variables one wishes t...The Gauss-Markov theorem assures us that the point estimate of the impact on the dependent variable derived by putting in the equation the hypothetical values of the independent variables one wishes to simulate will result in an estimate of the dependent variable which is minimum variance and unbiased.
- https://biz.libretexts.org/Workbench/MGT_235/06%3A_Confidence_Intervals/6.01%3A_IntroductionThe empirical rule, which applies to the normal distribution, says that in approximately 95% of the samples, the sample mean, \(\overline x\), will be within two standard deviations of the population ...The empirical rule, which applies to the normal distribution, says that in approximately 95% of the samples, the sample mean, \(\overline x\), will be within two standard deviations of the population mean \mu. Where \(\overline x\) is the sample mean. \(Z_{\alpha}\) is determined by the level of confidence desired by the analyst, and \(\sigma / \sqrt{n}\) is the standard deviation of the sampling distribution for means given to us by the Central Limit Theorem.
- https://biz.libretexts.org/Courses/Gettysburg_College/MGT_235%3A_Introductory_Business_Statistics_(2nd_edition)/06%3A_Confidence_Intervals/6.01%3A_IntroductionThe empirical rule, which applies to the normal distribution, says that in approximately 95% of the samples, the sample mean, \(\overline x\), will be within two standard deviations of the population ...The empirical rule, which applies to the normal distribution, says that in approximately 95% of the samples, the sample mean, \(\overline x\), will be within two standard deviations of the population mean \(\mu\). Where \(\overline x\) is the sample mean. \(z_\frac{\alpha}{2}\) is determined by the level of confidence (1-\(\alpha\)) desired by the analyst, and \(s / \sqrt{n}\) is the standard deviation of the sampling distribution for means given to us by the Central Limit Theorem.
- https://biz.libretexts.org/Courses/Gettysburg_College/MGT_235%3A_Introductory_Business_Statistics_(2nd_edition)/06%3A_Confidence_Intervals/6.02%3A_A_Confidence_Interval_for_a_Population_Standard_Deviation_Known_or_Large_Sample_SizeThe error bound - also known as the margin of error - gets its name from the recognition that it provides the boundary of the interval derived from the standard error of the sampling distribution. Bec...The error bound - also known as the margin of error - gets its name from the recognition that it provides the boundary of the interval derived from the standard error of the sampling distribution. Because the sample size is in the denominator of the equation, as \(n\) increases it causes the standard deviation of the sampling distribution to decrease and thus the width of the confidence interval to decrease.
- https://biz.libretexts.org/Courses/Gettysburg_College/MGT_235%3A_Introductory_Business_Statistics_(2nd_edition)/06%3A_Confidence_Intervals/6.03%3A_A_Confidence_Interval_for_a_Population_Standard_Deviation_Unknown_Small_Sample_CaseThe Student's t-distribution has more probability in its tails than the standard normal distribution because the spread of the t-distribution is greater than the spread of the standard normal. So the ...The Student's t-distribution has more probability in its tails than the standard normal distribution because the spread of the t-distribution is greater than the spread of the standard normal. So the graph of the Student's t-distribution will be thicker in the tails and shorter in the center than the graph of the standard normal distribution.
- https://biz.libretexts.org/Workbench/MGT_235/06%3A_Confidence_Intervals/6.02%3A_A_Confidence_Interval_for_a_Population_Standard_Deviation_Known_or_Large_Sample_SizeA confidence interval for a population mean with a known population standard deviation is based on the conclusion of the Central Limit Theorem that the sampling distribution of the sample means follow...A confidence interval for a population mean with a known population standard deviation is based on the conclusion of the Central Limit Theorem that the sampling distribution of the sample means follow an approximately normal distribution.
- https://biz.libretexts.org/Workbench/MGT_235/06%3A_Confidence_Intervals/6.03%3A_A_Confidence_Interval_for_a_Population_Standard_Deviation_Unknown_Small_Sample_CaseThis is another example of one distribution limiting another one, in this case the normal distribution is the limiting distribution of the Student's t when the degrees of freedom in the Student's t ap...This is another example of one distribution limiting another one, in this case the normal distribution is the limiting distribution of the Student's t when the degrees of freedom in the Student's t approaches infinity. The Greek letter \(\nu\) (pronounced nu) is placed in the general formula in recognition that there are many Student \(t_{\nu}\) distributions, one for each sample size. \(\nu\) is the symbol for the degrees of freedom of the distribution and depends on the size of the sample.
