Question

Suppose we have an existing confidence interval for a population mean. If we increase the sample size by a factor of 100, what happens to the width of the confidence interval?

a) It remains the same.

b) It decreases by a factor of 100.

c) It increases by a factor of 10.

d) It decreases by a factor of 10.

Answer 1

$C.I=\bar{X}\pm Z_\alpha /2\frac{\sigma }{\sqrt{n}}$

when n is increased by 100 factor then

$\sqrt{100}=10$

it will be decreased by a factor of 10