Let’s carefully analyze the problem and fill in the blanks based on the provided data.

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Key Information:

1. Null and Alternative Hypotheses (H₀ and H₁):

   • You are testing whether the herb affects the number of days with fever. Since the wording states "affects" without specifying direction (increase or decrease), this is a two-tailed test.
   • Correct choice: D. H₀: μ₁ = μ₂, H₁: μ₁ ≠ μ₂.

2. Test Statistic:

   • Given as -1.80.

3. P-value:

   • Given as 0.072.

4. Significance Level (α):

   • Stated as 0.01.

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Decision Rule:

• If the P-value is less than the significance level (α = 0.01), reject the null hypothesis (H₀). Otherwise, fail to reject H₀.

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Conclusion:

• Since P-value (0.072) > α (0.01), we fail to reject the null hypothesis.

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Filled Blanks:

1. First Blank: Fail to reject the null hypothesis.
2. Second Blank: Insufficient evidence to support the claim that the herb affects the number of days with fever.

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Final Answer:

• The herb does not appear to be effective in changing the number of days with fever at the 0.01 significance level.

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Would you like me to provide additional clarification or explore related questions? Here are some further questions we could discuss:

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1. Why do we use a two-tailed test instead of a one-tailed test here?
2. How is the P-value calculated in this scenario?
3. What would happen if we changed the significance level to 0.05 instead of 0.01?
4. What assumptions underlie the t-test used here?
5. How could increasing the sample size impact the results of this test?

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Tip: Always compare the P-value to the chosen significance level before deciding whether to reject the null hypothesis!