When the sample size is small
2
The standard deviation would generally decrease because the large the sample size is, the more we know about the population, so we can be more exact in our measurements.
In general the mean of a truly random sample is not dependent on the size of a sample. By inference, then, so is the variance and the standard deviation.
The standard deviation of the population. the standard deviation of the population.
If the population standard deviation is sigma, then the estimate for the sample standard error for a sample of size n, is s = sigma*sqrt[n/(n-1)]
Standard error of the sample mean is calculated dividing the the sample estimate of population standard deviation ("sample standard deviation") by the square root of sample size.
No, it is not.
When the sample size is small
The standard error is the standard deviation divided by the square root of the sample size.
yes
2
No.
The standard deviation would generally decrease because the large the sample size is, the more we know about the population, so we can be more exact in our measurements.
A single observation cannot have a sample standard deviation.
In general the mean of a truly random sample is not dependent on the size of a sample. By inference, then, so is the variance and the standard deviation.
The increase in sample size will reduce the confidence interval. The increase in standard deviation will increase the confidence interval. The confidence interval is not based on a linear function so the overall effect will require some calculations based on the levels before and after these changes. It would depend on the relative rates at which the change in sample size and change in standard deviation occurred. If the sample size increased more quickly than then standard deviation, in some sense, then the size of the confidence interval would decrease. Conversely, if the standard deviation increased more quickly than the sample size, in some sense, then the size of the confidence interval would increase.