Question

10) Empire airlines flies two engine aircraft. At times the engines fail in flight and the aircraft can fly with only one functioning engine, but they need at least one. The maintenance department of Empire airlines has a goal to have at least 97% of the engines working at any time in flight. If they are not meeting this goal they have to perform additional preventative maintenance on the engines. The maintenance crew chief took a random sample of 400 engines and found that 384 of them worked properly on their most recent flight a) The maintenance department will run a hypothesis test to determine if they can conclude they are not meeting their goal. What are the hypotheses, test statistic and distribution of the test statistic for this test? Would you reject or fail to reject the null hypothesis at a.01? What is the p-value for the test in part a? Should the maintenance crew chief be more concerned with Type l error or Type ll error in this test and why? What implications does this have for how the maintenance crew chief might choose the significance level for the test in part a? b) c)

Answer 1

Ans:

H₀:p>=0.97

H_a:p<0.97

We will use normal distrution for sampling diatribution of sample proportions.

sample proportion=384/400=0.96

a)Test statistic:

z=(0.96-0.97)/sqrt(0.97*(1-0.97)/400)

z=-1.172

critical z value=-2.33

As,z=-1.172>-2.33,we fail to reject null hypothesis.

b)p-value=P(z<-1.172)=0.1205

c)They should be concerned about type II error(as in part a we fail to reject null hypothesis.)

As,we fail to reject null hypothesis i.e. p>=0.97,but in actual it may not be true and it may cause risk.

So,they should choose the high significance level e.g. 0.15 instead of 0.01,then critical z value will be -1.036,and we will be able to reject null hypothesis.