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I need some help regarding a calculation that I need to be able to do only with a basic calculator of a proportion test:

A statistician is choosing a sample of 200 seeds. If 155 of these 200 are growing, what is the 95 confidence interval of the growing seeds ?

  • A) (0.726; 0.824)
  • B) (0.717;0.833)
  • C) (0.706;0.844)
  • D) (0.713;0.844)
  • E) (0.726;0.833)

So the formula is : $\frac{155}{200}+1.96\sqrt{ \frac{\frac{155}{200} \frac{45}{200}}{200} }$

I know the answer is the answer B. But what I can’t figure out is a way to compute it manually with a simple calculator (without any square root function on it and without Excel).

Maybe there should be a trick to find out which interval is the right one.

Information:

  • It tried to use approximation series to get a result, but it does not seem to be either reliable or practical.

  • I know the answer cannot be D or E. because the interval is not centered on 0.775 (155/200).

But how to determine it is B and not A or C ?

Any help would be appreciated.

XCoder
  • 482

1 Answers1

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It is $\frac{155}{200}=0.775$. And $\sqrt{\frac{155}{200}\cdot \frac{45}{200}\cdot \frac{1}{200}}\approx \sqrt{ 0.000871975} \approx \sqrt{0.0009} $

You should know, that $\sqrt{0.0009} = 0.03$

Now your calculator is able to calculate $0.775 + 1.96 \cdot 0.03=0.8338$

callculus42
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