From a sample of 100 Bloemfontein car commuters, the sample mean time to commute to work daily was found to be 35.8 minutes. It is known that the population standard deviation is 20 minutes.

Question

4.1 Find the standard error

Answer 1

To calculate the standard error (SE) of the mean, you can use the following formula:

\[ SE = \frac{\sigma}{\sqrt{n}} \]

Where:

• \(\sigma\) is the population standard deviation,
• \(n\) is the sample size.

In this case:

• \(\sigma = 20\) minutes,
• \(n = 100\).

Now, substituting the values into the formula:

\[ SE = \frac{20}{\sqrt{100}} = \frac{20}{10} = 2 \]

So, the standard error of the mean is 2 minutes.