Question

A researcher assumes that the standard deviation of the weekly sugar consumption in children in the community is 100g.

How large a sample is needed to estimate mean sugar consumption in the community with a margin of error of 10g at 95% confidence?

How many children should be studied if the researcher is willing to accept a margin of error of 25 at 95% confidence?

Answer 1

The margin of error(ME) is given as-

Using this formula of margin of error(ME) and after rearranging the formula we write the sample size as-

Now the standard deviation is and also we have given the margin of error for 95% confidence as

Calculation for the sample size (n) : When

Z-value for 95% confidence is-

So we need a sample size of in order to estimate the mean sugar consumption in the community with a margin of error of 10g with 95% confidence.

Calculation for the sample size (n) : When

So we need a sample size of in order to estimate the mean sugar consumption in the community with a margin of error of 25g with 95% confidence.