MHB Getting ready for the final, don't understand how to answer these

[chriskeller1]

Please please urgent help needed with questions like these

How do I predict how big the sample needs to be?

View attachment 3688

 

[MarkFL]

Regarding confidence intervals for one mean or proportion, we are given that the maximum error $E$ of the estimate for $\mu$ is:

$$E=z_{\alpha/2}\cdot\frac{\sigma}{\sqrt{n}}$$

So, by what factor must $n$ increase so that $E$ is one-fifth as large?

 

[chriskeller1]

Regarding confidence intervals for one mean or proportion, we are given that the maximum error $E$ of the estimate for $\mu$ is:

$$E=z_{\alpha/2}\cdot\frac{\sigma}{\sqrt{n}}$$

So, by what factor must $n$ increase so that $E$ is one-fifth as large?

n must be 5000 right?

 

[MarkFL]

n must be 5000 right?

Yes, because $n$ is under a radical, it must increase by a factor of $5^2=25$ in order for $E$ to be 1/5 as large. and so we find:

$$200\cdot25=5000$$