The Professor's Response

Dear Prof,

As I am finishing up studying, I had a question on 7.3. I reviewed when confidence level goes up the interval width increases and vise versa and that when sample size gets larger the confidence width gets smaller. Also, what can cause margin of error to increase and decrease. But I wanted to know on Now You Try It! For section 7.3 number 4 I am still a little confused about why increasing the confidence level requires a larger sample size?

The exact question was: What effect does choosing a higher confidence level have on the required sample size needed to estimate a mean within a given margin of error and having a given standard

deviation?

Answer: . Increasing the confidence level will increase the required sample size.

Thank you for all your help this semester,

Natalie R.

See the professor's answer below.

Hi Natalie,

**The question reads:** What effect does __choosing a higher confidence level__ have on the required sample size needed to estimate a mean within a given margin of error and having a given standard deviation?

Whenever you increase the confidence level, you will increase the margin of error or width of the confidence interval. Width and margin of error are virtually the same, since the width is just 2*margin of error, so if the margin of error gets larger the width gets larger. The only way to counteract the widening effect of increasing the confidence level is to increase the sample size. Increasing the sample size reduces the margin of error (width), so if we increase the sample size we will counteract the effect of increasing the confidence level.

There are two ways to __reduce__ the width or error in a confidence interval: 1) reduce the confidence level and 2) increase the sample size.

Hope that helps,

Professor McGuckian