Question

3. A random sample of 64 lighting flashes in a certain region resulted in a sample average radar echo duration of 0.7 sec and a sample standard deviation of 0.32 sec.

• (a) Construct a 89% confidence interval for the true mean radar echo duration.

• (b) Explain the meaning of your interval in such a way that someone who had not ever studied statistics would understand.

• (c) At a 0.11 level of significance, can you conclude that the true radar echo duration differs from 0.78 sec? Explain why

Answer 1

Answer:-

Given That:-

A random sample of 64 lighting flashes in a certain region resulted in a sample average radar echo duration of 0.7 sec and a sample standard deviation of 0.32 sec.

(a) Construct a 89% confidence interval for the true mean radar echo duration.

Here sample size is 64 so we will use z distribution to find CI

z value for 1.599 as P(-1.599<z<1.599)=0.89

So Margin of Error is

E = 0.064

Hence CI is

(b) Explain the meaning of your interval in such a way that someone who had not ever studied statistics would understand.

The confidence interval gives the range in which population parameter lies

Hence here average rada echo duration for population will lie in the range 0.636 to 0.764

(c) At a 0.11 level of significance, can you conclude that the true radar echo duration differs from 0.78 sec? Explain why

As range does not include 0.78, we conclude that it differs from 0.78 sec

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