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n automobile manufacturer claims that its van has a 37.4 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 280 vans, they found a mean MPG of 37.8. Assume the standard deviation is known to be 2.3. A level of significance of 0.05 will be used. Find the value of the test statistic. Round your answer to 2 decimal places.

Respuesta :

Answer:

Then z(s) is out of the acceptance region, we reject H₀,  doubts of the independent testing firm are valids

Step-by-step explanation:

We will develop a Hypothesis Test ( a 2 tail test since the independent testing firm is interested in finding out  if there is an incorrect MPG rating from the manufacturer

Test Hypothesis :

Null hypothesis                             H₀            μ    =    μ₀

Alternative Hypothesis                Hₐ             μ    ≠    μ₀

Significance Level   α  = 0,05    α/2  =  0,025

z(c) for α/2   from z-table      z(c)  = - 1, 96   and by symmetry  z(c) = 1,96

Calculating  z(s)

z(s) =  ( μ  -  μ₀ ) / σ /√n

z(s) = ( 37,8 - 37,4 ) / 2,3 /√280

z(s) = 0,4 * 16,73 / 2,3

z(s) = 2,90

Comparison between z(c)  and  z(s)

z(s) > z(c)       2,90 > 1,96

Then z(s) is out of the acceptance region, we reject H₀,  doubts of the independent testing firm are valids

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