Question

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 1

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

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