Question

A random sample of 110 lightning flashes in a certain region resulted in a sample average radar echo duration of .81 sec and a sample standard deviation of .34 sec. Calculate a 99% (two-sided) confidence interval for the true average echo duration μ, and interpret the resulting interval.

Answer 1

From the given information, \(n=110, \bar{x}=0.81\) and \(s=0.34\)

The sample size is, \(n \geq 30\), so we use \(Z\) - test.

The \(Z\)-critical value at the \(99 \%\) confidence level is, \(2.576 \quad\) (From normal tables)

Find the \(99 \%\) confidence interval for the true mean echo duration \(\mu\).

$$ \begin{aligned} 99 \% C . I &=\bar{x}-Z_{\text {critical }}\left(\frac{s}{\sqrt{n}}\right)<\mu<\bar{x}+Z_{\text {ctitical }}\left(\frac{s}{\sqrt{n}}\right) \\ &=0.81-2.576\left(\frac{0.34}{\sqrt{110}}\right)<\mu<0.81+2.576\left(\frac{0.34}{\sqrt{110}}\right) \\ &=0.81-0.083<\mu<0.81+0.083 \\ &=(0.727<\mu<0.893) \end{aligned} $$

Hence, the required confidence interval is, \(0.727<\mu<0.893\)