According to the Bureau of Labor and Statistics, the number of full-time employed, part-time employed, and unemployed adults in the United States in 2015 were 121,492,000, 27,341,000, and 8,297,000, respectively.t You believe that the rates in your community are different than the national averages, so you sample 260 adults age 18 and older and ask them to comment on whether they are employed full-time or part-time, or are currently unemployed. (a) Find the expected proportions for each of the employment categories. (Round your answers to three decimal places.) full-time employed part-time employed unemployed (b) The null hypothesis for the chi-square goodness-of-fit test comparing observed proportions of employment across categories versus the expected proportions from the national averages would be which of the following? O Ho:P1 = 201, P2 = 45, and P3 = 14 O Ho: P1 = 121,492,000, P2 = 27,341,000, and P3 = 8,297,000 Ho:P, = 0.773,P2 = 0.174, and P3 = 0.053 O Ho:P, = 77.3, P2 = 17.4, and Pg = 5.3 (c) A chi-square goodness-of-fit test produces a P-value of 0.03. Which of the following conclusions is appropriate? O Fail to reject the null hypothesis at or = 0.05 level. O Reject the alternate hypothesis at or = 0.05 level. Accept the null hypothesis at o = 0.05 level. Reject the null hypothesis at a = 0.05 level. [2/9 Points] DETAILS PREVIOUS ANSWERS DIEZSTAT4 6.3.033. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER A professor using an open source introductory statistics book predicts that 60% of the students will purchase a hard copy of the book, 25% will print it out from the web, and 15% will read it online. At the end of the semester he asks his students to complete a survey where they indicate what format of the book they used. Of the 127 students, 74 said they bought a hard copy of the book, 29 said they printed it out from the web, and 24 said they read it online. (Use a significance level of 0.05.) (a) State the hypotheses for testing if the professor's predictions were inaccurate. O Ho: H hard copy = H print = H online H: at least two of the group means, It hard copy' At print' A online' are not equal O Ho: H hard copy * H print * H online HA: at least two of the group means, It hard copy. It print' A online' are equal Ho: The distribution of the format of the book used by the students follows the professor's predictions. HA: The distribution of the format of the book used by the students does not follow the professor's predictions. O Ho: The distribution of the format of the book used by the students does not follow the professor's predictions. HA: The distribution of the format of the book used by the students follows the professor's predictions (b) How many students did the professor expect to buy the book? students How many students did the professor expect to print the book? students How many students did the professor expect to read the book exclusively online? students (c) This is an appropriate setting for a chi-square test. Check if the conditions required for a test are satisfied. (Select all that apply.) The success-failure condition is satisfied. The success-failure condition is not satisfied. The students were not sampled randomly, so we cannot be sure the independence condition is satisfied. Each expected count is greater than 5. The students were sampled randomly, so the independence condition is satisfied. X (d) Calculate the chi-squared statistic. (Round your answer to two decimal places.) Calculate the degrees of freedom. Calculate the p-value. (Round your answer to three decimal places.) p-value =
