Using the formula for margin of error as
MOE = z * σ / √n
would be very difficult since we are not given the value of the standard deviation. Standard deviation value must be given since it is obtained from the experiment.
However, we use another formula for MOE in the form of:
MOE = z sqrt [p (1 – p) / n]
where p is the proportion at 99% confidence interval at z crit value. From the standard distribution tables, this corresponds to a p value of:
z crit = 2.58
p = 0.9951
Therefore the margin of error is:
MOE = 2.58 sqrt [0.9951 (1 – 0.9951) / 670]
MOE = 6.96 x 10^-3 = 0.00696 s
We can see that at 99% Confidence interval, the Margin of Error is extremely small (almost 0). For the sake of calculation:
Confidence interval = 4.7 s ± 0.00696 s
Confidence interval = 4.69304, 4.70696
