Practice Standard Error in Statistics
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
The standard error (SE) is the standard deviation of a sampling distribution, measuring how much a sample statistic (like the sample mean) typically varies from the true population parameter across repeated samples. It decreases as sample size increases.
Standard error tells you how much your sample estimate might be 'off' from the true value. Larger samples have smaller SE because they're more precise - like asking 1000 people vs 10.
Example 1
easyA population has a standard deviation of \sigma = 20. If you take a random sample of n = 100, what is the standard error of the sample mean?
Example 2
mediumHow does the standard error change when you quadruple the sample size from n = 25 to n = 100? Assume \sigma = 30.
Example 3
mediumA researcher measures the reaction time of 64 participants and finds a sample standard deviation of s = 40 ms. Calculate the standard error and construct an approximate 95% confidence interval if the sample mean is 250 ms.
Example 4
hardA polling company wants the standard error of a proportion to be no more than 0.02 (2%). If a preliminary estimate suggests \hat{p} \approx 0.5, what minimum sample size is needed? Use SE = \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}.