Final Answer:
Based on ethnicity perform a goodness-of-fit test to determine whether the local results follow the distribution of U.S. AP examinee population b) The local results do not follow the distribution of U.S. AP examinee population. Therefore the correct answer is option b.
Step-by-step explanation:
A goodness-of-fit test assesses the agreement between observed data and the expected distribution. In this case, the null hypothesis (\(H_0\)) would be that the local results follow the distribution of the U.S. AP examinee population based on ethnicity.
The alternative hypothesis (H_a) would be that the local results do not follow this distribution. The test statistic, often chi-square
, is calculated by comparing the observed frequencies in each category with the expected frequencies based on the U.S. AP examinee population distribution.
If the calculated
value exceeds a critical value from the chi-square distribution or if the p-value is less than the chosen significance level (e.g., 0.05), we reject the null hypothesis.
This indicates that there is a significant difference between the observed and expected distributions, suggesting that the local results do not follow the distribution of the U.S. AP examinee population. Therefore, the correct answer is option (b) – "The local results do not follow the distribution of U.S. AP examinee population."
Conducting a thorough goodness-of-fit test involves obtaining data on the ethnicity distribution of the U.S. AP examinee population, collecting local results, calculating expected frequencies, and performing statistical calculations.
The decision to reject or not reject the null hypothesis is based on the results of these calculations and is crucial in understanding the representativeness of the local results in comparison to the broader U.S. AP examinee population. Therefore the correct answer is option b.