Please state more clearly what you are trying to do, because I think you may be confused as to what a confidence interval for a sample mean is :)

Suppose you drew a random, unbiased sample of 50 items from a normally distributed population. Further suppose the following:

The confidence interval for your sample mean is a function of the sample mean, the sample standard deviation, and the confidence level.

Based on the above, first you would compute the standard error:

=sample_std_dev / sqrt(sample_size)

=15 / sqrt(50)

~ 2.12

Next, find the t value associated with 95% confidence and 50 degrees of freedom. This is about 2.01.

Multiply the two to get your margin of error, which in this example is ~ 4.26.

Now, your confidence interval is (sample mean) +/- (margin of error), or 95.74 - 104.26.

What this means is that we expect that there is a 95% chance that the true population mean is a value within the range 95.74 - 104.26.

Taking a bigger sample is not going to increase your confidence level. Rather, having a larger sample,

*ceteris paribus*, makes the width of the confidence interval narrower.

Please see the attached file for an example of how I would do this.

Q-28009322.xlsx

Patrick