Final answer:
The exercise involves setting up a null hypothesis and an alternative hypothesis for a statistical test comparing the annual expenditure on prescription drugs per person in the Midwest to that in the Northeast.
Step-by-step explanation:
The question relates to formulating hypotheses for a statistical test to determine whether the population annual expenditure for prescription drugs per person is lower in the Midwest than in the Northeast of the United States. For statistical hypothesis testing, we would set up a null hypothesis (H0) and an alternative hypothesis (Ha). The null hypothesis typically states that there is no effect or no difference, while the alternative hypothesis represents what we are trying to prove, in this case, that the population annual expenditure is lower in the Midwest.
The null hypothesis (H0) would be: “The population annual expenditure for prescription drugs per person in the Midwest is equal to or higher than in the Northeast.” Mathematically, this could be stated as μMidwest ≥ μNortheast.
The alternative hypothesis (Ha) would be: “The population annual expenditure for prescription drugs per person in the Midwest is lower than in the Northeast.” Mathematically, this is μMidwest < μNortheast. To test these hypotheses, we would use the given sample data and population standard deviation to perform a one-tailed z-test, as the population standard deviation is known.