To test whether the mean value of a population is smaller than 3, the hypotheses should be structured to reflect that your null hypothesis assumes the mean is greater than or equal to 3, and the alternative hypothesis assumes the mean is less than 3.

The correct setup is:

• Null Hypothesis (H₀): μ ≥ 3 (The mean is greater than or equal to 3)
• Alternative Hypothesis (Ha): μ < 3 (The mean is less than 3)

This is a one-tailed test where you are testing if the population mean is less than 3.

Correct Answer:

• H₀: μ ≥ 3, Ha: μ < 3

Would you like more details or have any questions?

Here are 8 related questions to expand on this concept:

1. How do you determine the critical value for a one-tailed hypothesis test?
2. What is the significance level, and how does it influence hypothesis testing?
3. How do you interpret a Type I error in the context of this hypothesis test?
4. What is the difference between one-tailed and two-tailed p-values?
5. How can you increase the power of a hypothesis test?
6. What assumptions must be satisfied for conducting a one-sample t-test?
7. How does the choice of significance level (e.g., 0.05 vs. 0.01) affect the results of the test?
8. What are the potential consequences of rejecting the null hypothesis incorrectly?

Tip: When setting up your null and alternative hypotheses, ensure that the direction of the inequality in the alternative hypothesis matches the research question you are trying to answer.