This is a Statisitcs problem and im unsure to which test i am supposed to run. Please Help?

Question

 Kindergarten children have heights distributed N(39,2) inches. A kindergarten teacher believes that her class of 12 with a sample mean of 40.8 inches is statistically larger than stated value. Run a complete, appropiate test at the alpha=0.05 to determine if her belief is true or not.

Answer 1

H₀: µ=39

H_a: µ>39

Since σ=2 is known, use the z-test:

z=(40.8-39)/(2/√12)=3.118

 

P(z≥3.118)=9.114*10^-4.

 

Since P<0.05, you reject the null hypothesis at the α=0.05 level. The result is significant even at the .1%-level.