The correct answer is one-sample proportion z-test.
To assess whether the graduation rate of high-school students participating in sports differs from the known national graduation rate, the appropriate statistical test is the one-sample proportion z-test. This test is designed for situations where you have a sample proportion that you want to compare to a known or hypothesized population proportion.
In this case, the null hypothesis would be that the graduation rate of students participating in sports is equal to the national graduation rate, and the alternative hypothesis would suggest a difference. After collecting data on the graduation rates of the sampled students, you can calculate the sample proportion and use it to perform the one-sample proportion z-test.
The two-sample t-test and the matched pairs t-test are not suitable for this scenario because they are used when comparing means, not proportions. The one-sample t-test is also not appropriate as it is designed for comparing a sample mean to a known or hypothesized population mean. The two proportion z-test is used when comparing two independent sample proportions, which is not the case here.
In summary, the most appropriate test for comparing the graduation rate of students in sports to the national rate is the one-sample proportion z-test.
Therefore, the correct option is one-sample proportion z-test.