Trouble with Hypothesis testing (Psych. Stats)

#1
I'm still really sketchy on hypothesis testing, even after reading the chapter in my book twice and watching the video lecture for this topic twice. I have several practice problems that I've tried doing, but I'm really not sure what I'm doing wrong.

This is one of the problems that I have as an example:

The running time for 137 rats in a 6-foot runway is recorded. The data are ΣX = 1781 seconds and ΣX² = 25,345. Assume that μ = 11.5 seconds. Test Ho.

I know that part of testing the hypothesis is running a t-test, and I've got this formula for that:

t= mean of sample - mean of population/standard deviation of the sample

The calculation I get for t doesn't match the answer that the book gives, though. Also, once I get the t value, what am I supposed to do next?

I got the entire rest of this section, but this part is still giving me trouble. I know that the answer for this problem is:

t(136)=4.41, p<.01. The rats took significantly longer than 11.5 seconds to traverse the runway.

If someone could tell me step by step how to get from the above question to that answer, I'd be grateful.
 

JohnM

TS Contributor
#2
The sample mean is = 1781/137 = 13.

The sample standard deviation, s, uses ΣX = 1781 and ΣX² = 25,345 in the "computational" formula, which can be found here:
http://www.psych.utah.edu/gordon/Classes/Psych_3000_90/Lectures/EstimatingParameters/EstimatingParameters.htm

You should get:
s = sqrt[ (25345 - (1781^2/137)) / 136 ]
s = 4.015

Ho: mu = 11.5
Ha: mu <> 11.5
alpha = .01

t = (x - mu) / (s / sqrt(n))
t = (13.0 - 11.5) / (4.015 / sqrt(137))
t = 4.373

Since this t is larger than the critical (table) value of t:
t(.01, 136 d.o.f.) = 2.61

then you can reject Ho.