## Related questions with answers

An IRS research found that the average time for taxpayers to prepare, copy, and electronically file a 1040 tax form is 330 minutes. The standard deviation for this time distribution, which is normal, is 80 minutes. A group of 40 taxpayers are chosen at random by a consumer protection organisation. What is the standard error of the mean in this example?

Solution

VerifiedThe population mean $\mu$ is a parameter that indicates the average of the entire population. Its estimator is the sample proportion $\overline X$ and the estimate, or its particular value, is $\overline x$. Since $\overline X$ is a random variable whose value depends on the chosen random sample, then we need to discuss its sampling distribution.

The given population has a **normal distribution**. As such, the sampling distribution of the sample mean, regardless of the size, will also be normal.

The standard error of the sample mean indicates the variability across multiple samples in the population. This is computed using the formula

$\sigma _{\overline x} = \dfrac{\sigma}{\sqrt n}, \tag 1$

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