We want to calculate the maximum error of estimate E for the mean number of times high school seniors go out for lunch per week. The maximum error of estimate E is given by the following formula.
E = z * s/sqrt(n)Notice the mean is not needed to calculate the maximum error of estimate. The z-value corresponds to a particular confidence level, s is the standard deviation of the sample, and n is the sample size. Let's begin by finding the z-value that corresponds to the given confidence level. The table shows the most commonly used levels and corresponding z-values.
Confidence Level
z-value
90 %
1.645
95 %
1.960
99 %
2.576
We want to use 90 % confidence level, so from the table we know z will be equal to 1.645. A sample consists of 145 high school seniors, therefore n = 145. A standard deviation of 0.7 is given, so consequently s = 0.7. We are ready to calculate the maximum error of estimate E.
