To analyze the problem and select the appropriate null ($H_0$) and alternative ($H_1$) hypotheses, let us interpret the question:

The herb is being tested for its effect on reducing the number of "days with fever." This implies we are testing whether the mean number of fever days for children treated with the herb ($\mu_1$) is less than the mean number of fever days for children given the placebo ($\mu_2$).

Hypotheses

• Null Hypothesis ($H_0$): The herb does not reduce the number of fever days, meaning $\mu_1 = \mu_2$.
• Alternative Hypothesis ($H_1$): The herb reduces the number of fever days, meaning $\mu_1 < \mu_2$.

This aligns with a left-tailed test.

Correct Answer

The correct choice is: D. $H_0: \mu_1 = \mu_2$, $H_1: \mu_1 < \mu_2$.

Let me know if you'd like to further explore this analysis or perform additional calculations for this hypothesis test.

5 Related Questions:

1. What statistical test should be used to compare the means of two independent groups when variances are not assumed equal?
2. How do you calculate the test statistic for a two-sample t-test?
3. What does a significance level ($\alpha = 0.10$) imply for hypothesis testing?
4. How would you interpret a $p$-value smaller than the significance level?
5. How can sample sizes impact the results of a hypothesis test?

Tip:

When comparing two groups, always verify assumptions about normality and equality of variances to determine the appropriate statistical test.