A researcher is investigating the frequency of homes being hit by lightning. Sup

Question

A researcher is investigating the frequency of homes being hit by lightning. Suppose that (unbeknownst to the researcher) 1 out of 200 houses per year are struck by lightning. How large a sample size does the researcher need for the standard deviation of a sample proportion of lightning strikes per year to be no larger than 0.001? How can we interpret the number 0.001 above? It estimates the typical difference between the number of lightning strikes per year and 200. It estimates the typical difference between a sample proportion and 1/200. It estimates the typical number of lightning strikes per year. It estimates the typical distance between two lightning strikes. If the researcher wanted the standard deviation above to be half as large (to be 0.0005), how much larger would the sample size need to be? times as large.

Explanation / Answer

Result:

a).

p=1/200 =0.005

sd=sqrt(p(1-p)/n)

sqrt(0.005*0.995/n) =0.001

n = 0.005*0.995/0.001^2

=4975

b).

It estimates the typical difference between a sample proportion and 1/200

c).

sqrt(0.005*0.995/n) =0.0005

n = 0.005*0.995/0.0005^2

=19900

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