Question

The mean of a population being sampled is 64, and and the standard deviation is 6.

If the sample size is 50, the standard error of the mean is
. (Round off your answer to the nearest hundredth.)

Answer 1

The condition you need to meet in order to use a z*-value in the margin of error formula for a sample mean is either: 1) The original population has a normal distribution to start with, or 2) The sample size is large enough so the normal distribution can be used (that is, the Central Limit Theorem applies ). In general, the sample size, n, should be above about 30 in order for the Central Limit Theorem to be applicable. Now, if it’s 29, don’t panic — 30 is not a magic number, it’s just a general rule of thumb. (The population standard deviation must be known either way.)

Answer 2

The standard error of the mean is 0.85.

Explanation:

Given : The mean of a population being sampled is 64, and and the standard deviation is 6. If the sample size is 50.

To find : The standard error of the mean ?

Solution :

The mean of the population is
`\mu=64`

The standard deviation is
`\sigma=6`

The sample size is n=50

Standard error of the mean is defined as the standard deviation of the original distribution upon root of the sample size.

i.e.
`SE=(\sigma)/(√(n))`

`SE=(6)/(√(50))`

`SE=(6)/(7.071)`

`SE=0.848`

Therefore, The standard error of the mean is 0.85.