# Specify critical region, calculate the test stat?

• Apr 7th 2009, 08:13 PM
rba_mandy
Specify critical region, calculate the test stat?
Ok the question says:
Specify the critical region and calculate the test statistic based on data in the table below:
Ho: $\displaystyle \mu$ =75
Ha: $\displaystyle \mu$ < 75
alpha = .05
n = 64
$\displaystyle \bar{x}$ =72.7
$\displaystyle \sigma$ = 8.6

Here is what I have come up with, I am really confused so I'm not even sure if it's relevant.

z' = $\displaystyle \bar{x}$ - $\displaystyle \mu$ (all over) $\displaystyle \sigma$ / square root n
z' = -2.1395

With z-test I found that p = .0162

I'm not sure where to go from here or if I'm even heading in the right direction. Please and thank you for the help (Happy)
• Apr 8th 2009, 05:14 PM
matheagle
the test stat is correct
next with your Ha and alpha the rejection region is $\displaystyle (-\infty , -1.645)$.
So, your test stat is in the RR and you should reject Ho and accept Ha.
The p-value is $\displaystyle P(Z<-2.13953884)$.
• Apr 9th 2009, 11:47 AM
rba_mandy
THANK YOU! I understand now (Nod)