Engineers wish to collect data on the number of kilometres t

Engineers wish to collect data on the number of kilometres that a new engine design can pull a load using just one litre of fuel. The current design is known to pull the load a mean distance of 175 km on one litre of fuel and the designers wish to see if the new design is better, using a random sample of size 16. Assume that it is known from past experience that the standard deviation on pulling distances is equal to 8 km.

a) What hypotheses should be tested?

b) Suppose that the designers decide that their critical region is ¯x > 180 km; i) What is the probability of a type I error? ii) What is the probability that we fail to reject Ho even if the true mean is 183 km?

Solution

a)
Test Used: Z-Test For Single Mean
b)
Set Up Hypothesis
Null Hypothesis H0: U>180
Alternate Hypothesis H1: U<180
Test Statistic
Population Mean(U)=180
Given That X(Mean)=175
Standard Deviation(S.D)=8
Number (n)=16
we use Test Statistic (Z) = x-U/(s.d/Sqrt(n))
Zo=175-180/(8/Sqrt(16)
Zo =-2.5
| Zo | =2.5

i)
TYPE I Error : P-Value : Left Tail - Ha : ( P < -2.5 ) = 0.0062