A researcher examined the size of homes in a large urban sch

A researcher examined the size of homes in a large urban school district. In a random sample of 1600 homes, he found that the average size was 1952 square feet and the sample standard deviation was 1565 square feet. Calculate the margin of error for a 90% confidence interval.

Solution

To compute the margin of error, we need to find the critical value and the standard error of the mean. To find the critical value, we take the following steps.

Next, we find the standard error of the mean, using the following equation:

SE_x = s / sqrt( n ) = 1565 / sqrt( 1600 ) = 1565 / 40 = 39.125

And finally, we compute the margin of error (ME).

ME = Critical value x Standard error = 1.645 * 39.125 = 64.36

This means we can be 90% confident that the average school size in the urban is 1952 plus or minus 64.36, since the margin of error is 64.36.