StatisticsdrillStandard error of the mean
A statistics problem from Statisticsdrill. Solve it with one answer box, with a fresh sample on every attempt and the worked steps and spreadsheet function in the answer, and it is checked the moment you submit.
The task
Order values at an online store have a population standard deviation of σ = 15 dollars. You will take a random sample of n = 400 and compute the sample mean. By the central limit theorem, what is the standard deviation of the sample mean (its standard error)? Round to 3 decimal places.
What this problem teaches
The formula: SE = σ / √n. The sample mean varies less than single values because high and low draws cancel. Four times the sample size halves the standard error. With σ unknown, use s / √n instead.
A hint if you get stuck
SE = σ / √n. Averaging n values shrinks the spread by the square root of n, not by n.
Try it now, free, no account needed
The first 15 tasks on Statisticsdrill are free. Open it on the practice page, solve it, and get instant feedback with a hint. A free account adds the worked solution; Pro unlocks every task, timed mode and the certificate.
Open this problemMore problems in Distributions
- Binomial: exactly k
- Binomial: at least k
- Binomial standard deviation
- Poisson: exactly k
- Poisson: at most k
- Normal: between two values
- Normal: above a value
- Normal: percentile cutoff
- Sampling distribution of the mean
- Normal approximation to the binomial
- Continuous uniform: between two values
- Exponential: waiting longer than a time
- Sampling distribution of a proportion
- Poisson: rescaling the rate