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.
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 $0.775 + 1.96 \cdot 0.03=0.8338$