Question

An automobile manufacturer claims that its jeep has a 37.8 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the MPG for this jeep since it is believed that the jeep has an incorrect manufacturer's MPG rating. After testing 240 jeeps, they found a mean MPG of 37.9. Assume the variance is known to be 4.41. A level of significance of 0.02 will be used. Find the value of the test statistic. Round your answer to 2 decimal places.

Enter the value of the test statistic.

Answer 1

0.74

Explanation:

An automobile manufacturer claims that its jeep has a 37.8 miles/gallon (MPG) rating.

Given that rating of a jeep is on an average 37.8 miles/gallon and std deviation is sq rt of 4.41

Sample size = 240

Sample mean = 37.9

Significant level = 2%

Mean difference =
`=37.9-37.8=0.10`

Std error of sample =
`(s)/(√(n) ) =(√(4.41) )/(√(240) ) \\=0.1356`

Test statistic = Mean diff/std error

=
`(0.1)/(0.1356)\\ =0.7378`

Test statistic = 0.74 (rounding off to two decimals)