# Hypothesis Testing - Simple

How does hypothesis testing work with the standardized, normalized function in tables? In the left-hand graph, we have the normal curve of the actual problem. (The curve is centered at the hypothesized mean miH and the standard error is the standard deviation divided by the square root of n.) We calculate the critical value(s) for this curve using InverseNormal(miH,stderr,alpha/tailn) and InverseNormal(miH,stderr,1-alpha/tailn). Then we directly check our sample mean xbar to see if it is within (do NOT reject Ho) or outside (reject Ho). In the right-hand graph, we move to the standardized, normalized PDF (fs) and CDF (p) used in tables. We calculate the critical z value(s) using zc=InverseNormal(0,1,alpha/tailn). Automatically -zc is the other critical value. Then we offset our sample mean xbar . Here we used the formula directly offset=(difference in means)/stderr. (We could use ZMeanTest.) Finally, we check the offset to see if it is within (do NOT reject Ho) or outside (reject Ho).