Answer:
a) In the step-by-step-explanation
b) z(s) = -2.46 corresponding area is 0.0069
P [ μ₀ > 275 ] is 0.0069 or 0.69 %
We reject H₀
Step-by-step explanation:
Normal distribution
Random sample
size sample 78 = n
population standard deviation σ = 32
The school administrator declare that mean score is more (bigger than)
275. So the hypothesis test should be:
H₀ null hypothesis μ₀ > 275 and
Hₐ alternative hypothesis μ₀ < 275
Is one tail test with α = 0,04 from tables we have z(c) = - 176
We proceed to compute z(s)
z(s) = [ (μ - μ₀) /( σ /√n) ] ⇒ z(s) = (- 9 *√78 )/ 32
z(s) = - (9*8.83)/32
z(s) = - 2.46 corresponding area is 0,0069
P [ z > 275 ] = 0.0069 or 0.69 %
The value for z(s) = - 2.46 is smaller than the critical value mentioned in problem statement z(c) = - 1.74 , the z(s) is in the rejection zone
Therefore we reject H₀
