Hypothesis Testing of Plant Height

#1
Hello, I'm trying to figure out how to do hypothesis testing, working only from class notes, and the following example I just cannot follow.

" We collect a random sample of n =45 plants that we grow with a new treatmenta and observe a mean height of x-bar = 3.15cm, This is a point estimate for the true mean height of such plants. The null hypothesis is H0 : u = 20 and the alternative hypothesis is Ha : u > 20. The previous mean height using the old treatment was 20cm.

Suppose that we decide that to state that the data support Ha if x-bar >20 Suppose that H0 is true, what are our chances that we will conclude that the data support Ha? Then

P(X-bar > 20) = 1-P(X-bar < 20) which is approximately = 1 - "I with circle around the middle"(0) = 0.5 "



I follow everthing alright up until the calculation.... I know that it uses a z-table in some way, but I'm just not sure how! if X-bar is a normal random variable, then wouldn't you need at least need a standard deviation in order to perform the approximation?

Any help would be much appreciated! I've been poring over it for hours, and still can't get it. Thanks in advance!