Question

A random sample of 102 lightning flashes in a certain region resulted in a sample average radar echo duration of 0.86 sec and a sample standard deviation of 0.35 sec. Calculate a 99% (two-sided) confidence interval for the true average echo duration μ.

Answer 1

99% Confidence interval: (0.77,0.95)

Explanation:

We are given the following in the question:

Sample mean,
`\bar{x}` = 0.86 sec

Sample size, n = 102

Alpha, α = 0.01

Sample standard deviation, s = 0.35 sec

Degree of freedom =

`= n -1\\=102-1\\=101`

99% Confidence interval:

`\bar{x} \pm t_(critical)\displaystyle(s)/(√(n))`

Putting the values, we get,

`t_(critical)\text{ at degree of freedom 101 and}~\alpha_(0.01) = \pm 2.6253`

`0.86 \pm 2.6253((0.35)/(√(102)) )\\\\ = 0.86 \pm 0.0909\\\\ = (0.7691 ,0.9509)\approx (0.77,0.95)`

(0.77,0.95) is the required 99% confidence interval for the true average echo duration μ.