Final answer:
For evaluating the weight loss program's claim of mean weight loss of at least 10 pounds after 1 month, the null hypothesis (H0) would be μ ≤ 10, and the alternative hypothesis (Ha) would be μ > 10. Hypothesis testing involves looking for evidence to reject the null hypothesis in favor of the alternative.
Step-by-step explanation:
To test the claim that program participants have a mean weight loss of at least 10 pounds after 1 month, we must formulate the null and alternative hypotheses. The null hypothesis (H0) is a statement of no effect or no difference, and it will be tested against an alternative hypothesis (H1 or Ha) that states what we suspect might actually be true.
Null and Alternative Hypotheses:
H0: μ ≤ 10 - The null hypothesis states that the mean weight loss is less than or equal to 10 pounds, implying that the weight loss program does not lead to results greater than 10 pounds on average.
Ha: μ > 10 - The alternative hypothesis states that the mean weight loss is greater than 10 pounds, supporting the weight loss program's claim.
It's important to note that in hypothesis testing, we do not prove a hypothesis but rather look for evidence against the null hypothesis. If there is significant evidence, we may reject the null hypothesis in favor of the alternative hypothesis.