1. ## What is "unusual"?

When we choose whether a value of the mean (x bar) is "unusually" far from the mean (mu) is a matter of choosing whether:

(x bar - mu)/(sigma/root(n)) is "unusually" far from zero.

The concern is, what is "unusual"?

It it were defined as "occuring on less than 5 % of occassions"
• what range of values of (x bar - mu)/(sigma/root(n)) would be regarded as unusually far from zero?

• what would this range be if we replace 5% by 1%?

2. Originally Posted by nacknack
When we choose whether a value of the mean (x bar) is "unusually" far from the mean (mu) is a matter of choosing whether:

(x bar - mu)/(sigma/root(n)) is "unusually" far from zero.

The concern is, what is "unusual"?

It it were defined as "occuring on less than 5 % of occassions"
• what range of values of (x bar - mu)/(sigma/root(n)) would be regarded as unusually far from zero?

• what would this range be if we replace 5% by 1%?
Because you are talking about a sample mean and I am ging to assume a large sample:

$z=\frac{\overline{x}-\mu}{(\sigma/\sqrt{n})}$

has (approximatly) a standard normal distribution. Now look up the critical value $z_{crit}$ for 5% and 1% (that is $z_{crit}=P^{-1}(0.95)$ and $z_{crit}=P^{-1}(0.99)$ where $P$ is the cumulative distribution function for the standard normal distribution), and then any value of $z$ greater than this is "unusual"

CB