Question

An automobile manufacturer claims that their van has a 46.4 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the MPG for this van. After testing 140 vans they found a mean MPG of 46.0. Assume the standard deviation is known to be 2.6. Is there sufficient evidence at the 0.02 level that the vans underperform the manufacturer's MPG rating? Step 2 of 5: Enter the value of the z test statistic. Round your answer to two decimal places.

Answer 1

given data are

population mean = 46.4 miles/gallon

sample n =140

sample mean = 46.0

population sd = 2.6

null hypothesis H0: - = 46.4

alternative hypothesis Ha :- < 46.4

= level of significance =0.02

test statistic: - z=

z=(46.0 - 46.4)/(2.6/ )

= - 0.4/ 0.2197

= - 1.8203

= - 1.82

decision rule:- at 2% level from z table z= -2.05

reject H0 if zcal < - 2.05

decision :- zcal> z

i.e, -1.82> -2.05, so fail to reject the null hypothesis H0

conclusion: - at 2% level their is no sufficient evidence to support the claim that " the vans under perform the manufacturers MPG rating"