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Does confidence interval only for normal distribution?
No, it doesn’t, although it might well be. Just as there are many possible samples that you might have taken, but didn’t, there are many possible confidence intervals you might have constructed around the sample means, but couldn’t.
How do you calculate confidence interval?
You can see how sample variability affects the confidence intervals. In four random samples (shown in red) the values in the sample are so extreme that the confidence interval does not include the population mean. Thus the estimate of the coverage probability is 96/100 = 96% for these 100 samples.
What does TOBT the value indicate?
the probability of making a Type I error will not equal a. What does the tobt value indicate? How far the sample mean is from the population mean of the sampling distribution in estimated standard error units. The estimated standard error of the mean.
How to calculate the coverage probability of a confidence interval?
Simulate many samples of size n from the population. Compute the confidence interval for each sample. Compute the proportion of samples for which the (known) population parameter is contained in the confidence interval. That proportion is an estimate for the empirical coverage probability for the CI. You might wonder why this is necessary.
What is the empirical coverage probability of the CI?
This graph shows why the term “coverage probability” is used: it is the probability that one of the vertical lines in the graph will “cover” the population mean. The previous simulation confirms that the empirical coverage probability of the CI is 95% for normally distributed data.
Is the coverage probability always 0.95 in a simulation?
Isn’t the coverage probability always (1-α) = 0.95? No, that is only true when the population is normally distributed (which is never true in practice) or the sample sizes are large enough that you can invoke the Central Limit Theorem. Simulation enables you to estimate the coverage probability for small samples when the population is not normal.
How to calculate the population coefficient of variation?
The population coefficient of variation is defined as a ratio of the population standard deviation to the population mean given by. The typical sample estimate of is given as where is the sample standard deviation, the square root of the unbiased estimator of population variance, and is the sample mean.