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.

(a) Calculate a 99% confidence interval for the true average echo duration.

(b) 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

Mean = 0.81

Sample size (n) = 110

Standard deviation (s) = 0.34

Confidence interval(in %) = 99

z @ 99.0% = 2.576

Since we know that

Required confidence interval

Required confidence interval = (0.81-0.0835, 0.81+0.0835)

Required confidence interval = (0.7265, 0.8935)

b)

Since for width of 0.1 margin of error(M.E.) will be 0.1/2 = 0.05

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