Answer:
The answers to the questions are
(a) P = 0.0176
(b) P = 0.5
(c) P = 0.0571
Step-by-step explanation:
The P value is the calculated probability of obtaining extreme reults which are as extreme as observed res ult when the study null hypothesis H₀ is true
The p value is given by
P ( = 185 when μ = 175)
z =
z( = 185) =
= 1.5811
Therefore the P ( = 185 when μ = 175) = P(z = 1.5811)
0.94295
The probability density function is
Therefore the probability is
= 0.0176
b) The type II error is given by
β = P(type II error) = P(Fail to reject the null hypothesis when it is false)
Therefore
β = P ( < 185 when μ = 185)
P, which gives
P(z<0) and β = 0.5
(c) For true mean foam height of 195 mm we have
β = P ( < 185 when μ = 195)
and P
Which gives P(z < -1.58)
From z table the probability is β = 0.0571