Writing Hypotheses: Medicine A medical research team is investigating the mean cost of a 30-day supply of a heart medication. A pharmaceutical company thinks that the mean cost is less than \$60. You want to support this claim. How would you write the null and alternative hypotheses?

Verified step by step guidance

1. Understand the context: The null hypothesis (H₀) represents the default or status quo assumption, while the alternative hypothesis (Hₐ) represents the claim you want to support. In this case, the pharmaceutical company claims that the mean cost is less than \$60.
2. Define the population parameter: Let μ represent the mean cost of a 30-day supply of the heart medication.
3. Write the null hypothesis (H₀): The null hypothesis assumes that the mean cost is not less than \$60. Mathematically, this is written as H₀: μ ≥ 60.
4. Write the alternative hypothesis (Hₐ): The alternative hypothesis supports the claim that the mean cost is less than \$60. Mathematically, this is written as Hₐ: μ < 60.
5. Verify the hypotheses: Ensure that the null and alternative hypotheses are mutually exclusive and collectively exhaustive, meaning they cover all possible scenarios for the mean cost (μ).

Key Concepts

Null Hypothesis (H0)

The null hypothesis is a statement that indicates no effect or no difference, serving as a default position that there is no relationship between two measured phenomena. In this context, it would assert that the mean cost of the heart medication is equal to or greater than $60, which the pharmaceutical company is trying to challenge.

Alternative Hypothesis (H1)

The alternative hypothesis is a statement that contradicts the null hypothesis, suggesting that there is an effect or a difference. In this scenario, the alternative hypothesis would claim that the mean cost of the heart medication is less than $60, which is the assertion the medical research team aims to support.

Hypothesis Testing

Hypothesis testing is a statistical method used to make decisions about the validity of a hypothesis based on sample data. It involves calculating a test statistic and comparing it to a critical value to determine whether to reject the null hypothesis in favor of the alternative hypothesis, thus providing evidence for the claim being investigated.