I am currently studying statistics on MIT open course. And I have a question about Z test. Below is the example of IQ test.
H0 = MIT student IQs are distributed identically to the general population = MIT IQ’s follow a N(100, 15^2) distribution.
HA = MIT student IQs tend to be higher than those of the general population = the average MIT student IQ is greater than 100.
And significance level is 0.05
I was wondering if mean and standard deviation of population are given, why can't you just directly calculate the probability of 112 from the population distribution? I can simply type in given information in R. pnorm(x=112, mean=100, sd=225) gives me probability density of IQ 112 or below on the normal distribution with mean 100 and sd 225. So why is the answer not simply 1-pnorm(x=112, mean=100, sd=225)?