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What happens to the t statistic when using a larger sample?
Higher t-value means lower p-value infering that the difference between sample-mean ($\bar{X}$) and population-mean ($\mu$) is significant (hence we reject the null hypothesis). But this formula seems counter-intuitive to me as bigger sample size (higher $n$) should give sample mean closer to population mean.
Does sample size affect T value?
t-Distributions and Sample Size The sample size for a t-test determines the degrees of freedom (DF) for that test, which specifies the t-distribution. The overall effect is that as the sample size decreases, the tails of the t-distribution become thicker.
How is sampling variance related to population mean?
That can, indeed, be affected by the sample design. But, using the appropriate estimator, you can estimate the population variance of that characteristic using the variability that characteristic in the sample. Sampling variance is something else. We have the population mean, ¯¯¯¯Y Y ¯.
What happens to sample size as sample size grows?
So as the sample size grows, the closer your estimated variance will be to the true variance. Another way of thinking of this is that if you have observed all observations in the population, you will know the true variance. If you observe all observations except one, you will still have a extremely good estimate.
How does sample size affect precision of standard errors?
To illustrate how sample size affects the calculation of standard errors, Figure 1 shows the distribution of data points sampled from a population (top panel) and associated sampling distribution of the mean statistic (bottom panel) as sample size increases (columns 1 to 3).
How to find sampling distribution of sample mean?
Now that we’ve got the sampling distribution of the sample mean down, let’s turn our attention to finding the sampling distribution of the sample variance. The following theorem will do the trick for us! S 2 = 1 n − 1 ∑ i = 1 n ( X i − X ¯) 2 is the sample variance of the n observations.