Final answer:
To calculate standard error for constructing a confidence interval, one must know if the population standard deviation is available. The standard error is computed from the standard deviation divided by the square root of the sample size and multiplied by the critical Z or T value, then rounded to the nearest whole number.
Step-by-step explanation:
To find the standard error of the sampling distribution for constructing a confidence interval, we first need to know if we have the population standard deviation or if we are using a sample standard deviation. If the population standard deviation is known and the sample size is large enough (typically n > 30), we use the Z-distribution which follows the standard normal distribution. On the other hand, if the population standard deviation is unknown and we are using the sample standard deviation, we use the T-distribution, accounting for the sample size through degrees of freedom.
For either distribution, the standard error (SE) is calculated using the formula:
SE = standard deviation / sqrt(n)
Where 'n' is the sample size. Once the SE is calculated, it is multiplied by the appropriate Z or T score - depending on the confidence level and the distribution being used - to construct the confidence interval. We would round the final value of the standard error to the nearest whole number as requested.
If we were provided with an explicit sample mean, sample standard deviation, and sample size (or population standard deviation for a large enough sample), we could calculate the confidence interval by finding the margin of error and adding/subtracting it from the sample mean.