For a population with \( \sigma=10 \) an \( x \) calculated from a sample of 36 observations will have a standarderror = (Round to two decimals)

The standard error (SE) of the sample mean can be calculated using the formula: \[ SE = \frac{\sigma}{\sqrt{n}} \] where \( \sigma \) is the population standard deviation and \( n \) is the sample size. Here, we have \( \sigma = 10 \) and \( n = 36 \). Plugging in the values: \[ SE = \frac{10}{\sqrt{36}} = \frac{10}{6} \approx 1.67 \] So, the standard error is approximately **1.67**. --- In statistical practice, understanding standard error is crucial—it helps researchers determine how well their sample represents the population. A smaller standard error indicates the sample mean is likely closer to the population mean, which is generally what we want! A common mistake is confusing standard deviation with standard error. While standard deviation measures the spread of individual scores in a population, standard error pertains to the accuracy of the sample mean estimate. Always remember: the SE gets smaller with larger samples!