Question

) A random sample of 110 lighting flashes in a certain region resulted in a sample average radar echo duration of 0.81 sec and a sample standard deviation of 0.34 sec. Calculate 99% (two-sided) confidence interval for the true average echo duration µ.

Answer 1

99% (two-sided) confidence interval for the true average echo duration µ is

(0.73<µ<0.89)

Explanation:

Confidence Interval can be calculated using M±ME where

• M is average radar echo duration (0.81 sec)

• ME is the margin of error from the mean

And margin of error (ME) around the mean can be calculated using the formula

ME=
`(z*s)/(√(N) )` where

• z is the corresponding statistic in 99% confidence level(2.58)

• s is the standard deviation of the sample(0.34)

• N is the sample size(110)

Then ME=
`(2.58*0.34)/(√(110) )` ≈0,084

99% Confidence interval would be 0.81±0,08 or (0.73, 0.89)