Question

13. A poll conducted by the General Social Survey asked 1155 people whether they thought that people with high incomes should pay a greater or smaller percenta low-income people. The results are presented in the table ge of their income in tax than Category Pay much more Observed 218 Pay somewhat more 497 425 Pay the same Pay less 15 Five years earlier, it was determined that 18.5% believed the rich should pay much more, 39.2% believed they should pay somewhat more. 41.2% believed they should pay the same, and 1.1 believed they should pay less. Can we conclude that the current percentages differ from these? Use the a 0.05 level of significance. (12 points)

Answer 1

"""Pay Much More"" Null H_0: - P_1 = P_01 where P_1 current year sample proportion. Alternate H_a: - P_1 isnotequalto P_01 P_01: - 5 yrs earlier population proportion Test statistic: - Z_1 = P_1 - P_01/P_1 sigma P_1 = 218/1155 = 0.1887: P_0 = 0.185: P_1 sigma = squareroot P_1(1 - P_1)/1155 = 0.0115 Z_1 = 0.1887 - 0.185/0.0115 = 0.321 alpha = 0.05 rightdoublearrow for 2-failed test Z_critical = 1.96 therefore Z_1 < Z_critical rightdoublearrow We accept H_0. ""Pay Somewhat More"" Null H_0: - P_2 = P_02: P_2 = 497/1155 = 0.43 Alternate H_a: P_2 isnotequalto P_02 P_02 = 0.392 Test Z_2 = P_2 - P_02/ squareroot P_2(1 - P_2)/1155 = 2.6098: at alpha = 0.05 Z_critical = 1.96 \r\n at alpha = 0.05: Z_critical < Z_2 < rightdoublearrow We reject Null H_0 ""Pay Somewhat More""category does differ significantly ""Pay the Same"" Null H_0: -P_3 = P_03 Alternate H_a: - P_3 isnotequalto P_03: P_3 = 425/1155 = 0.3679: P_03 = 0.412 therefore observe Test start Z_3 = 0.3679 - 0.412/ squareroot 0.3679(1 - 0.3679)/1155 Z_3 = (-3.108) "