Question

A random sample of 81 lighting flashes in a certain region resulted in a sample average radar echo duration of 0.8168 sec and a sample standard deviation of 0.36 sec (“Lighting Strikes to an Airplane in a Thunderstorm”, Journal of Aircraft, 1984). Calculate a 99% (two-sided) confidence interval for the true average echo duration μ.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 0.8168 sec

sample standard deviation = s = 0.36 sec

sample size = n = 81

Degrees of freedom = df = n - 1 = 81 - 1 = 80

At 99% confidence level the t is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

t _/2,df = t_0.005,80 = 2.639

Margin of error = E = t_/2,df * (s /n)

= 2.639 * (0.36 / 81)

= 0.1056

The 99% confidence interval estimate of the population mean is,

- E < < + E

0.8168 - 0.1056 < < 0.8168 + 0.1056

0.7112 < < 0.9224

(0.7112 , 0.9224)