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dangina [55]
2 years ago
6

After calculating the sample size needed to estimate a population proportion to within 0.05, you have been told that the maximum

allowable error (E) must be reduced to just 0.025. If the original calculation led to a sample size of 1000, the sample size will now have to be
Mathematics
1 answer:
Svetlanka [38]2 years ago
6 0

Answer:  40000

Step-by-step explanation:

The formula to find the sample size is given by :-

n=p(1-p)(\dfrac{z_{\alpha/2}}{E})^2, where p is the prior estimate of the population proportion.

Here we can see that the sample size is inversely proportion withe square of margin of error.

i.e. n\ \alpha\ \dfrac{1}{E^2}

By the equation inverse variation, we have

n_1E_1^2=n_2E_2^2

Given : E_1=0.05   n_1=1000

E_2=0.025

Then, we have

(1000)(0.05)^2=n_2(0.025)^2\\\\\Rightarrow\ 2.5=0.000625n_2\\\\\Rightarrow\ n_2=\dfrac{2.5}{0.000625}=4000

Hence, the sample size will now have to be 4000.

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