Question

Professor Graham wants to reduce the width of theconfidence interval around his estimate of the proportion ofadults who are carriers of a certain bacteria. What can hedo to accomplish this?

Answer 1

The formula of the confidence interval is:

`CI=\mu\pm\frac{zs}{\sqrt[]{n}}`

Where μ - mean, z-confidence level value, s-standard deviation, n-sample size

So, notice that we need to reduce the value of CI without modifying the value of μ, we want out the value of CI to be 'closer to that of μ

Let's analyze case by case:

increase the confidence level (z)

In this case, notice that the second term of the equation would be greater, and if it was 'separating' CI from the value of μ before, this contrast would be even greater.

So it's likely that the first option is not correct

Now, in the case of the second option:

if n becomes smaller so its square root. Furthermore, as sqrt(n) (square root of n) gets smaller, 1/sqrt(n) grows!

Regarding the third option (increase his sample size ):

Notice that if n grows, then sqrt(n) grows to, and then

So, the second term in the equation is greater and, similarly to the first option, this cannot be the right option.