Question

An automobile manufacturer has given its van a 28.2 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the actual MPG for this van since it is believed that the van has an incorrect manufacturer's MPG rating. After testing 180 vans, they found a mean MPG of 28.5. Assume the population standard deviation is known to be 2.1. A level of significance of 0.02 will be used. Find the value of the test statistic. Round your answer to two decimal places.

Answer 1

The Value of Z-statistic

Z = 1.923

Explanation:

Step(i):-

Given Population mean 'μ' = 28.2 miles / gallon

Given sample size 'n' = 180

Mean of the sample x⁻ = 28.5

Standard deviation of the Population 'σ' = 2.1

Level of significance = 0.02

Null hypothesis :H₀: x⁻ = μ

Alternative Hypothesis :H₁ : x⁻ ≠ μ

Step(ii):-

The Z-statistic

`Z = (x^(-)-mean )/((S.D)/(√(n) ) )`

`Z = (28.5-28.2)/((2.1)/(√(180) ) )`

Z = 1.923

The critical value

Z₀.₀₂ = 2.326

The calculated value Z = 1.923 < 2.326 at 0.02 level of significance

null hypothesis is accepted

There is no significance difference between independent testing firm and contracted to test the actual MPG