An automobile manufacturer claims that its jeep has a 31.231.2 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 230230 jeeps, they found a mean MPG of 31.431.4. Assume the standard deviation is known to be 2.52.5. A level of significance of 0.050.05 will be used. State the hypotheses.

Answer:We accept H₀, we don´t have evidence for rejecting H₀Step-by-step explanation:We have a Normal DistributionSize sample 230 jeeps        n = 230Testing 230 different jeeps means independent eventsWe formulate our test hypothesis  Null hypothesis                   H₀           ⇒    μ₀  =  31.2Alternative hypothesis         Hₐ           ⇒    μ₀   ≠ 31.2 Then we compute the z(s)  z statistics  as:z(s)  =  [ (μ - μ₀) /( σ/√n) ]                 ⇒   z(s)  = (0,2)* (√250) / 2.52z(s)  =  1,25Now we find z(c)  A level of significance is given  α = 0,05  but we are in the caseof two tail test therefore we work with  α/2    or   0,025 on both tailsIn z table the value of area 0,025 correspond to z(c) = 1.96We compare z(s)  and z(c)z(s)  = 1.25         z(c) =  1.96       ⇒     z(s) < z(c)That means z(s) is in the acceptance region we accept H₀