# Need direction - Hypothesis Testing

• Mar 1st 2011, 09:59 PM
yvonnehr
Need direction - Hypothesis Testing
I've worked through a set of practice questions and ran across this problem and don't see how I can solve it without $\displaystyle \sigma$. Can someone please give me some direction?

Q: When someone dials 911 for an emergency, the average length of time to reach an operator is supposed to be no more than 30 seconds. However, in a recent survey of 81 such calls, the sample mean came out to be 32 seconds. Is the response time in fact too long? Use $\displaystyle \alpha$=.10

So, $\displaystyle \mu_0$=30, $\displaystyle n$=81, and $\displaystyle \bar{x}$=32.
$\displaystyle H_o$:$\displaystyle \mu=30$, and
$\displaystyle H_a$:$\displaystyle \mu>30$.

I wanted to use the Z or T test statistics but I guess I can't because I don't see that I'm provided with enough information to be able to use them.

I really appreciate your help! I'm sure there is something basic that I'm not seeing.(Thinking)
• Mar 1st 2011, 10:14 PM
matheagle
I would venture to guess that is a poisson rv and thus the variance is the same as the mean.
(By the way I never sleep)
If these are Poisson's then you have as n goes to infinity

$\displaystyle {\bar X-\mu\over \sigma/\sqrt{n}}\to N(0,1)$

but we can use the Law of Large Numbers and Slutsky's Theorem.
There we have $\displaystyle \sigma^2=\mu=\lambda$

So If this is a Poisson we can use either $\displaystyle \bar X$ as estimate of $\displaystyle \sigma^2$
or use the null hypothesis value as the estimate of the unknown variance.

I'm making this guess since n is greater than 30 so I would guess they want to use the CLT.
And if there isn't a sigma, we need to find a relationship between moo and sigma.

Night Poisson Ivy
• Mar 2nd 2011, 11:16 AM
yvonnehr
Hi MathEagle!
It also seemed to me that the problem may involve a Poisson RV. But how can I argue that when I'm not given any time intervals or such?

Thanks! It's great to hear from you!

-Poisson Ivy
• Mar 2nd 2011, 11:57 AM
matheagle
maybe they just left out sigma?
so, how is Charms doing?
are you in school?