Final answer:
The most appropriate method for investigating the teacher's belief is hypothesis testing. We would set up a hypothesis test, calculate the test statistic and p-value, and interpret the results. If the p-value is less than the significance level, we reject the null hypothesis and conclude that the teacher's belief is supported.
Step-by-step explanation:
To investigate the teacher's belief, the most appropriate method is hypothesis testing. We can set up a hypothesis test to determine if the proportion of students in the teacher's district who participate in community service activities is greater than 28 percent. The null hypothesis, denoted as H0, would be that the proportion is equal to 28 percent, and the alternative hypothesis, denoted as Ha, would be that the proportion is greater than 28 percent.
Next, we would need to calculate the test statistic and p-value using the data from the teacher's sample. If the p-value is less than a chosen significance level (often 0.05), we would reject the null hypothesis and conclude that there is evidence to support the teacher's belief that the proportion is greater than 28 percent. If the p-value is greater than the significance level, we would fail to reject the null hypothesis and conclude that there is not enough evidence to support the teacher's belief.
Finally, we would interpret the results of the hypothesis test in the context of the problem and draw a conclusion about whether the rate of community service participation is indeed greater than 28 percent in the teacher's district.