The columns in the table below contain the Race/Ethnicity of U.S. Public Schools for a recent year, the percentages for the Advanced Placement Examinee Population for that class, and the Overall Student Population. Suppose the right column contains the result of a survey of 1,000 local students from that year who took an AP Exam. AP Examinee Population Overall Student Population Survey Frequency 113 Race/Ethnicity Asian, Asian American, or Pacific Islander 10.2% 5.4% Black or African-American 8.2% 14.5% 94 Hispanic or Latino 15.5% 15.9% 136 American Indian or Alaska Native White 0.6% 1.2% Not reported/other 59.4% 6.1% 61.6% 1.4% 10 604 43 Perform a goodness-of-fit test to determine whether the local results follow the distribution of U.S. AP examinee population, based on ethnicity. (Use a significance level of 0.05.) Part (a) State the null hypothesis. ○ The local results and the U.S. AP examinee population are independent events. The distributions of the local results and the U.S. AP examinee population are the same. The distributions of the local results and the U.S. AP examinee population are not the same. ○ The local results follow the distribution of the U.S. AP examinee population. ○ The local results do not follow the distribution of the U.S. AP examinee population. Part (b) State the alternative hypothesis. The local results and the U.S. AP examinee population are independent events. The distributions of the local results and the U.S. AP examinee population are the same. ○ The distributions of the local results and the U.S. AP examinee population are not the same. ○ The local results follow the distribution of the U.S. AP examinee population. The local results do not follow the distribution of the U.S. AP examinee population. Part (c) What are the degrees of freedom? (Enter an exact number as an integer, fraction, or decimal.) Part (d) State the distribution to use for the test. ○ to ○ t5 ○ x Ο χ Part (e) What is the test statistic? (Round your answer to two decimal places.) Part (f) What is the p-value? (Round your answer to four decimal places.) Explain what the p-value means for this problem. If Ho is false, then there is a chance equal to the p-value that the value of the test statistic will be equal to or greater than the calculated value. If Ho is true, then there is a chance equal to the p-value that the value of the test statistic will be equal to or greater than the calculated value. ○ If Ho is false, then there is a chance equal to the p-value that the value of the test statistic will be equal to or less than the calculated value. ○ If Ho is true, then there is a chance equal to the p-value that the value of the test statistic will be equal to or less than the calculated value. Part (g) Sketch picture of this situation. Shade the region(s) corresponding to the p-value. Part (h) p-value μ μ 1/2(p-value) p-value 1/2 p-value) μ μ 1/2(p-value) 1/2(p-value) Indicate the correct decision ("reject" or "do not reject" the null hypothesis), the reason for it, and write the appropriate conclusion. (i) Alpha (Enter an exact number as an integer, fraction, or decimal.) απ (ii) Decision: Oreject the null hypothesis O do not reject the null hypothesis (iii) Reason for decision: O Since a p-value, we do not reject the null hypothesis. ○ Since α > p-value, we reject the null hypothesis. ○ Since x < p-value, we do not reject the null hypothesis. (iv) Conclusion: There is sufficient evidence to conclude that the local results do not follow the distribution of the U.S. AP examinee distribution. There is not sufficient evidence to conclude that the local results do not follow the distribution of the U.S. AP examinee distribution.