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You are planning a survey with a 94% level of confidence in your finding. How large should your sample be so that the margin of error is at most 2.5%.

User CLearner
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1 Answer

9 votes

Answer: 1416

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Step-by-step explanation:

Usually a 95% level is standard for many stats problems like this. Unfortunately a 94% confidence level is a bit unusual. But you can use an inverse z calculator to determine that the z critical value is approximately z = 1.881

The error we want is E = 0.025 or smaller.

We don't know the sample proportion phat, but we can make the conservative estimate of phat = 0.5

Plug these values into the min sample size formula below

This formula applies to proportions (instead of the mean).

n = phat*(1-phat)*(z/E)^2

n = 0.5*(1-0.5)*(1.881/0.025)^2

n = 1415.2644 approximately

n = 1416 is the final answer

Always round UP to the nearest whole number when it comes to min sample size problems like this.

Side note: if you used z = 1.88, then it would lead to n = 1414. So it depends on how accurate of a z value you use that determines the final answer. Luckily, 1414 is fairly close to 1416. I'd stick with 1416.

User FBergo
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