Question

The results for all 10 grocery surveys were actually generated using a mathematical simulation, found on the Simulation tab of the spreadsheet. To use it, enter a population mean and population standard deviation in the two yellow cells at the top of worksheet and follow the instructions. Every time a new set of data is generated, the data changes, providing a new sample. You can copy this data and paste it into the histogram tool to analyze it. (You don't have to do that in this activity, but it's there for you to experiment with, if you like.) Any given set of sample data generated in this way would not typically have the same mean, distribution, and standard deviation as the population values, but the simulated sample data would be consistent with a randomly selected sample from such a population. Note that the simulated population mean is 1.73, and the simulated standard deviation is 0.657. Imagine that this random sample survey was simulated an infinite number of times. In that case, the population mean (1) of all the samples would be $1.73. All the sample means would be normally distributed, according to the central limit theorem. Question 1 If the standard deviation of the population is $0.657 (as it is in the simulation), what is the standard error of the mean? Round up your answer to the nearest tenth of a cent.

Answer 1

The standard error of the mean is given by:

$\frac{\sigma}{\sqrt[]{n}}$

where sigma is the standard deviation and n is the sample size. In this case the sample size is 10 and the standard deviation is 0.657, then the standard error is:

$\frac{0.657}{\sqrt[]{10}}=0.208$

Therefore the standard error is $0.208.