Question

A random sample of 101 lightning flashes in a certain region resulted in a sample average radar echo duration of 0.87 sec and a sample standard deviation of 0.40 sec. Calculate a 99% (two-sided) confidence interval for the true average echo duration μ. (Round your answers to two decimal places.) , Interpret the resulting interval. We are 99% confident that this interval contains the true population mean. We are 99% confident that this interval does not contain the true population mean. We are 99% confident that the true population mean lies above this interval. We are 99% confident that the true population mean lies below this interval.

Answer 1

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

0.87±0.10. (between 0.77 and 0.97 sec)

We are 99% confident that this interval contains the true population mean.

Explanation:

Confidence Interval can be calculated using M±ME where

• M is the sample average radar echo duration (0.87 sec)

• ME is the margin of error from the mean

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

ME=
`(z*s)/(√(N) )` where

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

• s is the standard deviation of the sample(0.40 sec)

• N is the sample size (101)

Then ME=
`(2.58*0.40)/(√(101) )`≈0.10

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

0.87±0.10.