Question 1201232
population mean is assumed to be 32 calories
sample size is 20
sample mean is 33.3
sample standard deviation is 2.5
standard error is standard deviation / square root of sample size = 2.5 / sqrt(20) = .5590169944.
test t-score is (x - m) / s = (33.3 - 32) / .5590169944 = 2.325510697
area to the right of that at 19 degrees of freedom is equal to .0156354548.
x is the sample mean
m is the assumed population mean
s is the standard error.
at .05 two tailed level of significance, this is less than .025, making the results of the test significant.
if you use critical t-score, that would be equal to 2.093024022.
since that is less than the test t-score of 2.32....., the results are, once again, significant, as they should be, because the critical t-score and the critical level of significance always give results that are consistent with each  other.