Question

QUESTION 5

1. The manufacturer of a new compact car claims that the car will average at least 35 miles per gallon in general highway driving.

   For 100 test runs, the car averaged 35.5 miles per gallon with a standard deviation of 4 miles per gallon.

   Suppose that the manufacturer tests the following hypotheses:

   

   

   Consider the 1% significance level. What is the power of the test if the actual average fuel efficiency is 36 miles per gallon?

   	a.	88.877%
   	b.	99.086%
   	c.	95.254%
   	d.	56.749%
   	e.	80.511%

Answer 1

solution:

true mean , µ =    36              
hypothesis mean,   µo =    35              
significance level,   α =    0.01              
sample size,   n =   100              
std dev,   σ =    4.0000              
δ=   µ - µo =    1              
std error of mean,   σx = σ/√n =    4.0000   / √    100   =   0.40000

Zα =       2.3263   (right tailed test)
POWER,   =   P(Z > Zα - δ/σx)                  
= P(Z > 2.326   - (   1   /   0.4000   ))
=P(Z> -0.174   )

=   0.56749  

so, power = 56.749%