## X^2 testing for standard deviation question: did I solve this right?

Q8. A standard UNIX program called “ping” was used to measure the connect time (in milliseconds) to contact and receive a reply from another computer on the Internet. The following connect times were noted:
350 1450 222 680 299 157 202 525 568 448
130 254 405 331 644 822 461 292 204 396
680 517 322 536 343 258 526 288 330 262
Assuming that the population of connect times is normally distributed, test the hypothesis that the population standard deviation of the connect times is less than 300 milliseconds. [10 points]
alpha = 0.05
what I did so far:
mean = 430.066
standard deviation = 257.672
n = 30
X^2 = [(n-1)s^2]/o^2 = [(30-1)257.672^2]/300^2 = 21.394
ignore the numbers, I can solve everything else. I just need to state the hypothesis and identify the claim so I can get the critical numbers. my guess:
hypothesis: s > or = 300ms
null hypothesis and claim: s < 300ms
critical value: 17.708
17.708 < 21.394
there is enough evidence to reject claim.
this is a yes or no question...