Final answer:
The hypothesis involves testing whether the true mean MPG of a car is 54.8 MPG, as claimed by the manufacturer, or different. This would be done through a hypothesis test comparing the claim to the results of independent testing.
Step-by-step explanation:
The hypothesis in question pertains to a claim by an automobile manufacturer regarding the miles per gallon (MPG) of a car. The manufacturer claims that the car has a 54.8 MPG rating, whereas independent testing found a mean MPG of 54.5 with a known variance of 4.41. To assess this claim statistically, one would set up a hypothesis test:
- Null Hypothesis (H0): The true mean MPG of the car is 54.8 MPG.
- Alternative Hypothesis (Ha): The true mean MPG of the car is not 54.8 MPG.
Using these hypotheses, a statistical test such as a Z-test or t-test could be performed to evaluate the likelihood of the observed mean MPG given the null hypothesis. Factors such as the sample size, mean, standard deviation, and significance level would be considered in making a decision whether to reject or not reject the null hypothesis.