Question

An automobile manufacturer claims that its car has a 37.9 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the MPG for this car since it is believed that the car has an incorrect manufacturer's MPG rating. After testing 140 cars, they found a mean MPG of 38.2. Assume the standard deviation is known to be 1.2. A level of significance of 0.01 will be used. Find the value of the test statistic. Round your answer to 2 decimal places

Answer 1

2.958

Explanation:

Sample mean (x) = 38.2 MPG

Population mean (μ) = 37.9 MPG

Sample size (n) = 140

Standard deviation (σ) = 1.2

The test statistic (Tstat) can be obtained thus :

(x - μ) / σ/sqrt(n)

Tstat = (38.2 - 37.9) / 1.2/sqrt(140)

Tstat = 0.3 / 0.1014185

Tstat = 2.9580401

Test statistic = 2.958