We want to calculate the maximum error of estimate for the time spent in the gym. The maximum error of estimate E is given by the following formula.
E = z * s/sqrt(n)Notice the mean time 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 95 % confidence level, so from the table we know z will be equal to 1.960. The survey asked 300 members of the fitness club, meaning that n = 300. A standard deviation of 8.6 minutes is given, so s = 8.6. We are ready to calculate the maximum error of estimate E.
