Answer:
There is not a convincing statistical evidence, at the significance level of a = 0.05, that the manager's belief is correct.
As the null hypothesis maybe false accepting it makes a type II error.
Step-by-step explanation:
Let the null and alternate hypotheses be
H0: p ≤ 0.4 vs Ha : p>0.4
q= 1-p= 1-0.4= 0.6
The significance level alpha is 0.05
The critical region for one tailed test is Z> ± 1.645
The sample proportion is p^= x/n= 38/90=0.42222
Using the z statistic
z= p^- p/ √pq
z= 0.422-0.4/ √0.4*0.6
z= 0.04536
Since the calculated value of z= 0.04536 does not lie in the critical region Z> ± 1.645 we fail to reject null hypothesis.
There is not sufficient evidence to support the manager's claim.
Type I error is when we reject the true null hypothesis .
Type II error is when we accept the false null hypothesis .
As the null hypothesis maybe false accepting it makes a type II error.
Answer:
420:8
Step-by-step explanation:
