Question

An automobile manufacturer claims that its van has a 44.3 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the MPG for this van since it is believed that the van has an incorrect manufacturer's MPG rating. After testing 130 vans, they found a mean MPG of 44.4. Assume the standard deviation is known to be 2.6. A level of significance of 0.05 will be used.

(a) Make a decision to reject or fail to reject the null hypothesis.

Answer 1

Explanation:

H0: u = 44.3

Hi : u# 44.3

Z1-0.05/2

Z1-0.025

Z0.975 = 1.96

Z = x-u/s.d/√n

Z= 44.4 -44.3/2.6/√130

Z = (0.1×11.4018)/2.6

Z=0.44

Since the calcalculated value is less than the table value and does not fall in the rejection region we fail to reject the null hypothesis