In an experiment using 30 mice, the sample proportion of the mice that gained weight after a drug injection is 0.65. What is the 99.7% confidence interval for the actual proportion in the population?

Guest Apr 14, 2015

#4**+5 **

I'm not a statistician as such so a proper one, (a proper statistician that is ), might take issue, however, so far as I'm aware, the S.E. that's being calculated here is the S.E. for the parent population, not the sample. We don't have a standard deviation for the sample.

BTW, this is the method used in opinion poles for elections and so on.

Bertie
Apr 17, 2015

#2**+5 **

The Standard Error for the proportion of weight gains in the whole population will be

$$\displaystyle \sqrt{\frac{0.65 \times 0.35}{30}}=0.087\quad \text{ 3 dp},$$

which means that the 99.7% confidence limits will be

$$\displaystyle 0.65 \pm 3\times 0.087 = 0.65 \pm 0.26.$$

Bertie
Apr 17, 2015

#3**+5 **

Thanks Bertie,

So the Standard Error of a Bernoulli distribution is just

$$SE=\sqrt{\dfrac{p*q}{n}}$$

(edited a little)

Melody
Apr 17, 2015

#4**+5 **

Best Answer

I'm not a statistician as such so a proper one, (a proper statistician that is ), might take issue, however, so far as I'm aware, the S.E. that's being calculated here is the S.E. for the parent population, not the sample. We don't have a standard deviation for the sample.

BTW, this is the method used in opinion poles for elections and so on.

Bertie
Apr 17, 2015