Question

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?
a: between 0.602 and 0.697
b: between 0.563 and 0.737
c: between 0.476 and 0.824
d: between 0.389 and 0.911

Answer 1

Answer:

The correct option is d.

Step-by-step explanation:

The formula for confidence interval for the actual proportion in the population is

$CI=p\pm z^*\sqrt{\frac{p(1-p)}{n}}$

Where, p is population proportion, n is sample size and z* is the tabulated value of z at given confidence interval.

The value of z* is 3 for 99.7% confidence interval.

$CI=0.65\pm 3\times \sqrt{\frac{0.65(1-0.65)}{30}}$

$CI=0.65\pm 3\times \sqrt{\frac{0.65(0.35)}{30}}$

$CI=0.65\pm 0.261247$

$CI=[0.65-0.261247,0.65+0.261247$

$CI=[0.388753,0.911247]$

$CI=[0.389,0.911]$

Therefore the 99.7% confidence interval for the actual proportion in the population is between 0.389 and 0.911. Option d is correct.

Answer 2

D: between 0.389 and 0.911