Standard Error Calculation Explained
The question asks for the standard error (SE) of the sample mean, given the sample size ($n$) and the population standard deviation ($\sigma$).
The formula used to calculate the standard error of the sample mean is:
$ SE = \frac{\sigma}{\sqrt{n}} $
Step-by-Step Calculation
- Identify Given Values:
- Sample size, $n = 25$
- Population standard deviation, $\sigma = 2$
- Apply the Formula: Substitute the given values into the standard error formula.
$ SE = \frac{2}{\sqrt{25}} $
- Calculate the Square Root: Find the square root of the sample size.
$ \sqrt{25} = 5 $
- Compute the Standard Error: Divide the population standard deviation by the square root of the sample size.
$ SE = \frac{2}{5} = 0.4 $
- Rounding: The result is 0.4. Rounded to one decimal place, it remains 0.4.
Therefore, the standard error of the sample mean is 0.4.
Important Questions from Sampling Theorems
In the construction of cost of living index, commodities are selected by:
If 4, 5, 6, 6, 6, 6, 6, 6, 6, 7 be a random sample from a Poisson population with parameter λ, then an unbiased estimate of λ is:
The data taken from the publication "sankhya" will be considered as:
A completely randomised design is based on the principles of ______ and randomisation only.
A sample of 30 latest returns on UTI stock reveals a mean return of $4 with a sample standard deviation of $0.13. The estimated standard error of the sample mean is:
