I post too much don't I? haha anyway, any help with this problem is appreciated.

"From a normal population, a sample with

N=4 is taken with sample mean M= 81 and sample standard deviation s = 10.42. For a null hypothesis = 92, calculate a t-score for the sample mean. What is the p-value for a two-tailed test? Based on the p-value, is the population mean significantly different from 92?"

Calculating a tscore for sample mean is: sample mean - null hypothesis/ standard error of the mean so 81-92/(10.42/(sqrt)5)= -2.36

Mr F says: n = 4 so won't it be (81-92)/(10.42/(sqrt)4)= -2.11 .....
P(-2.36<t<0)=0.4585. Thus, P(t<-2.36)=0.5-0.4585= 0.0415.

Mr F says: Where have you got these numbers from? They aren't correct (even allowing for the error in the t-value). Pr(t < -2.11) = 0.06268. I got this value using the t-distribution with 4 - 1 = 3 defrees of freedom.
Since this is a two-tailed test (it asked how the mean is different not less than or greater than) I double this amount?

Mr F says: Correct.
So is my p-value 0.2075? The last part of the question I always get stuck on (Based on the p-value, is the mean significantly different from 92) but I want to go with yes. ha. There's another question, but I'm stuck

"Based on the p-value you found above, can you conclude that the population mean is significantly different from 92 at 0.01 level? How about at 0.1 level?"