Question

Betty tabulated the miles-per-gallon values for her car as 26.5, 28, 30.2, 29.6, 32.3, and 24.7.

The standard error of the sample mean for this set of data is __________.


1.11


0.25


0.67


1.27

Answer 1

The standard error of the sample mean for this set of data is 1.11

Standard error of the mean

The formula for calculating the standard error of the sample mean is given as:

$e=\frac{\sigma}{\sqrt{n}}$

where;

• $\sigma$ is the standard deviation of the sample
• n is the sample size

Given the data samples 26.5, 28, 30.2, 29.6, 32.3, and 24.7, the standard deviation of the mean will be 2.73

The sample size n is 6

Substitute the given parameters into the formula to have:

$e=\frac{2.73}{\sqrt{6}}\\e=\frac{2.73}{2.449}\\e=1.11$

The standard error of the sample mean for this set of data is 1.11

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