The pop-o-matic company says there microwave popcorn leaves 15 kernels unpopped on average (they aren't sure though).  We KNOW that the standard deviation (sigma) of the number of kernels that don't pop is 10 (i.e., we KNOW the spread; we DON'T KNOW the mean for sure).

We observe 50, 40, 60, and 50 unpopped kernels.

What is x bar? 50

What is the standard deviation of the mean?

standard deviation of mean = 10/4^(1/2)= 5

What is the 95% confidence interval?

z(95%)=1.96

margin = 1.96*5 = plus or minus 9.8

Are the pop-o-matic people wrong?

Null Hypotheses: kernels equals 15
Alternative Hypothesis: kernels not equal to 15
 

(15-50)/5=-7

7 z-scores from the mean is about a zero chance.  More likely aliens will interrupt class.