a An example
... Sampling distributions The Central Limit Theorem Standard errors z-tests for sample means The 5 steps of hypothesis-testing Type I and Type II error ...
... Sampling distributions The Central Limit Theorem Standard errors z-tests for sample means The 5 steps of hypothesis-testing Type I and Type II error ...
5.7 Appendix: Using R for Sampling Distributions
... Thus, we have used the simulation capabilities of R to demonstrate visually (from the histograms) and numerically (from the realized variances) the impact of the sample size, n, on Var(X̄). We can also see an illustration of the Central Limit Theorem in the last histogram. With x̄ values computed fr ...
... Thus, we have used the simulation capabilities of R to demonstrate visually (from the histograms) and numerically (from the realized variances) the impact of the sample size, n, on Var(X̄). We can also see an illustration of the Central Limit Theorem in the last histogram. With x̄ values computed fr ...
Estimate
... Confidence level that “true” value is within 1 standard error (standard deviation of sampling distribution) from the sample mean is 0.6826. Probability that “true” value is within 2 standard error from the sample mean is 0.9545. What we did here is to find sample distribution and to use it to define ...
... Confidence level that “true” value is within 1 standard error (standard deviation of sampling distribution) from the sample mean is 0.6826. Probability that “true” value is within 2 standard error from the sample mean is 0.9545. What we did here is to find sample distribution and to use it to define ...
Simple Linear Regression
... Key Insight: To construct a prediction interval, we will have to assess the likely range of residual values corresponding to a Y value that has not yet been observed! We will build a probability model (e.g., normal distribution). Then we can say something like “with 95% probability the residuals wil ...
... Key Insight: To construct a prediction interval, we will have to assess the likely range of residual values corresponding to a Y value that has not yet been observed! We will build a probability model (e.g., normal distribution). Then we can say something like “with 95% probability the residuals wil ...
PACKET 6 - Variance and Standard Deviation
... data values. Because of this they have a huge effect on the mean and standard deviation. Therefore in many experiments and data sets the outlier is typically removed. But how do we decide what constitutes an outlier? One way is to look at data values that are more than 3 standard deviations away fro ...
... data values. Because of this they have a huge effect on the mean and standard deviation. Therefore in many experiments and data sets the outlier is typically removed. But how do we decide what constitutes an outlier? One way is to look at data values that are more than 3 standard deviations away fro ...
Example3_1
... If the salary distribution were skewed (for example, a few graduates received abnormally large salaries), the mean would be biased upward while the median would not be affected by the unusual values. ...
... If the salary distribution were skewed (for example, a few graduates received abnormally large salaries), the mean would be biased upward while the median would not be affected by the unusual values. ...
Power 10
... • Develop a model that has a theoretical basis. • Gather data for the two variables in the model. • Draw the scatter diagram to determine whether a linear model appears to be appropriate. • Determine the regression equation. • Check the required conditions for the errors. • Check the existence of ou ...
... • Develop a model that has a theoretical basis. • Gather data for the two variables in the model. • Draw the scatter diagram to determine whether a linear model appears to be appropriate. • Determine the regression equation. • Check the required conditions for the errors. • Check the existence of ou ...
The Central Limit Theorem (CLT)
... The Central Limit Theorem (CLT) is an extremely useful tool when dealing with multiple samples. Multiple samples and the Central Limit Theorem Consider a population of random variable x (we assume that variations in x are purely random – in other words, if we would plot a PDF of variable x, it w ...
... The Central Limit Theorem (CLT) is an extremely useful tool when dealing with multiple samples. Multiple samples and the Central Limit Theorem Consider a population of random variable x (we assume that variations in x are purely random – in other words, if we would plot a PDF of variable x, it w ...
Inference for Means Review
... P-value = 0; reject Ho since p-value < ; The data strongly supports the claim that the salinity level is higher in the winter. 7. one sample t-interval ; conditions: Random seedlings given; Independence is reasonable since one seedling’s height doesn’t affect another’s height. large enough sample s ...
... P-value = 0; reject Ho since p-value < ; The data strongly supports the claim that the salinity level is higher in the winter. 7. one sample t-interval ; conditions: Random seedlings given; Independence is reasonable since one seedling’s height doesn’t affect another’s height. large enough sample s ...
Bootstrapping (statistics)
In statistics, bootstrapping can refer to any test or metric that relies on random sampling with replacement. Bootstrapping allows assigning measures of accuracy (defined in terms of bias, variance, confidence intervals, prediction error or some other such measure) to sample estimates. This technique allows estimation of the sampling distribution of almost any statistic using random sampling methods. Generally, it falls in the broader class of resampling methods.Bootstrapping is the practice of estimating properties of an estimator (such as its variance) by measuring those properties when sampling from an approximating distribution. One standard choice for an approximating distribution is the empirical distribution function of the observed data. In the case where a set of observations can be assumed to be from an independent and identically distributed population, this can be implemented by constructing a number of resamples with replacement, of the observed dataset (and of equal size to the observed dataset).It may also be used for constructing hypothesis tests. It is often used as an alternative to statistical inference based on the assumption of a parametric model when that assumption is in doubt, or where parametric inference is impossible or requires complicated formulas for the calculation of standard errors.