Question

An automobile manufacturer has given its car a 46.2 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the actual MPG for this car since it is believed that the car has an incorrect manufacturer's MPG rating. After testing 240 cars, they found a mean MPG of 46.4 . Assume the population variance is known to be 2.56 . A level of significance of 0.05 will be used. State the null and alternative hypotheses.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 46.2
Alternative Hypothesis, Ha: μ ≠ 46.2

Rejection Region
This is two tailed test, for α = 0.05
Critical value of z are -1.96 and 1.96.
Hence reject H0 if z < -1.96 or z > 1.96

Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (46.4 - 46.2)/(1.6/sqrt(240))
z = 1.94

P-value Approach
P-value = 0.0524
As P-value >= 0.05, fail to reject null hypothesis.

cannot reject manufacturer's claim