Question

Consider two sample means distributions corresponding to the same x distribution. The first sample mean distribution is based on samples of size n=100 and the second is based on sample of size n=225.Which sample mean distribution has the smaller standard error? Please THOROUGHLY Explain and no pictures as it is hard for me to read some handwriting :) Thanks!

Answer #1

The formula for standard error is given by:

We have the same distribution for x. This means that the population standard deviation is going to be the same i.e. is going to be the same.

The first sample mean distribution has n=100

The second sample mean distribution has n=225

Clearly

Hence the second sample mean distribution has the smaller standard error.

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