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Pavlova-9 [17]
3 years ago
15

An automobile manufacturer claims that its jeep has a 31.231.2 miles/gallon (MPG) rating. An independent testing firm has been c

ontracted 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.
Mathematics
1 answer:
borishaifa [10]3 years ago
6 0

Answer:

We accept H₀, we don´t have evidence for rejecting H₀

Step-by-step explanation:

We have a Normal Distribution

Size sample 230 jeeps        n = 230

Testing 230 different jeeps means independent events

We formulate our test hypothesis

 Null hypothesis                   H₀           ⇒    μ₀  =  31.2

Alternative 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) / 2.52

z(s)  =  1,25

Now 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 tails

In z table the value of area 0,025 correspond to z(c) = 1.96

We 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

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