Question

A random sample of 110 lightning flashes in a certain region resulted in a sample average radar echo duration of 0.81 second and a sample standard deviation of 0.34 second. This sample data is used as a pilot study, and now the investigator would like to design a new study to construct a 99% confidence interval with width 0.1. What is the necessary sample size

Answer 1

`n=((2.58(0.34))/(0.05))^2 =307.79 \approx 308`

So the answer for this case would be n=308 rounded up to the nearest integer

Explanation:

The margin of error is given by this formula:

`ME=z_(\alpha/2)(s)/(√(n))` (a)

And on this case we have that ME =0.1/2 =0.05 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

`n=((z_(\alpha/2) s)/(ME))^2` (b)

The critical value for 99% of confidence interval now can be founded using the normal distribution since the sample size is large enough to assume the estimation of the standard deviation as the population deviation. The critical value for this case is
`z_(\alpha/2)=2.58`, replacing into formula (b) we got:

`n=((2.58(0.34))/(0.05))^2 =307.79 \approx 308`

So the answer for this case would be n=308 rounded up to the nearest integer