Question: A major car manufacturer wants to test a new engine to determine whether it meets ...
a) Using α = 0.05, exami.....
b) Construct a 99% confidence in...  Edit

Answer: H0: mu<20
H1 mu>=20

sample mean, x bar=(15.6 + 16.2 + 22.5+ 20.5+ 16.4 +19.4 + 16.6 + 17.9 + 12.7 + 13.9 +12.6)/11=16.75
sample sd=3.146
population sd= 2.99

sample size,n=11
sandard error=population sd/sqrt(n)=2.99/sqrt(11)=0.901

test statistic,z= (x bar- mu)/s.e= (16.75-20)/0.901=-3.06

at α = 0.05 , z-critical=+/- 1.65

hence , z-calculated(3.06) > z-critical.
Reject null.
engine does not meets the
pollution standard.(Ans.)

b) x bar =16.75
margin of error= population sd/sqrt(n)*z_c

z_c is the critical z at c% confidence.

Here z_c=2.58

margine of error,e= 0.901*2.58=2.325

Confidence interval=(x bar - e, x bar +e)=(16.75-2.325, 16.75+2.325)=(14.425, 19.075 ) (Ans.)  Edit