An automobile manufacturer claims that its van has a 27.6 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 210 vans, they found a mean MPG of 28.0. 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.
Accepted Solution
A:
Answer:Null Hypothesis: H₀: There is no difference between the sample mean and Population meanH₀ : x⁻ = μTest statistic Z = 2.5204 > 1.96 at 0.05 level of significance The null hypothesis is rejected at 0.05 level of significance There is a difference between the sample mean and Population meanStep-by-step explanation:Step(i):-Given mean of the Population = 27.6 miles/gallonSample size 'n' = 210Mean of the sample = 28.0 miles/gallonGiven the standard deviation of the population = 2.3Level of significance = 0.05The critical value Z₀.₀₅ = 1.96Step(ii):-Null Hypothesis: H₀: There is no difference between the sample mean and Population meanH₀ : x⁻ = μAlternative Hypothesis:H₁: There is a difference between the sample mean and Population meanH₁: x⁻ ≠ μTest statistic [tex]Z = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } } = \frac{28.0-27.6}{\frac{2.3}{\sqrt{210} } }[/tex] Z = 2.5204 Z = 2.5204 > 1.96 at 0.05 level of significance The null hypothesis is rejected at 0.05 level of significance There is a difference between the sample mean and Population mean