Please help me understand the following statistics problems:
DETAILS PREVIOUS ANSWERS MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER You may need to use the appropriate technology to answer this question. The sample data below represent the number of late and on time flights for three airlines. Airline Flight Late 57 69 On Time 243 231 326 (a) Formulate the hypotheses for a test that will determine if the population proportion of late flights is the same for all three airlines. OH: Not all population proportions are equal. Ha: P1 = P2 - P3 OHo: P1 = P2 = P3 He: All population proportions are not equal. O Ho: All population proportions are not equal. Ha: P1 = P2 = P HO: P1 - P2 - P3 He: Not all population proportions are equal. [b) Conduct the hypothesis test with a 0.05 level of significance. Find the value of the test statistic. (Round your answer to three decimal places.) Find the p-value. (Round your answer to four decimal places.) p-value = State your conclusion. O Reject Ho. We cannot conclude that not all of the population proportions are equal. O Reject Ho. We conclude that not all of the population proportions are equal. Do not reject Ho. We cannot conclude that not all of the population proportions are equal. O Do not reject Ho. We conclude that not all of the population proportions are equal. c) Compute the sample proportion of late flights for each airline. P1 P1 = What is the overall proportion of late flights for the three airlines? p - 2. DETAILS PREVIOUS ANSWERS MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER You may need to use the appropriate technology to answer this question. Benson Manufacturing is considering ordering electronic components from three different suppliers. The suppliers may differ in terms of quality in that the proportion or percentage of defective components may differ among the suppliers. To evaluate the proportion of defective components for the suppliers, Benson has requested a sample shipment of 500 components from each supplier. The number of defective components and the number of good components found in each shipment are as follows. Supplier Component Defective 17 22 Good 483 478 458 (a) Formulate the hypotheses that can be used to test for equal proportions of defective components provided by the three suppliers. O Ho: Not all population proportions are equal. He: PA = PD = P OHO: PA = Po = Pc My: All population proportions are not equal. O Ho: All population proportions are not equal. Ha: PA " PB = PC HO: PA - PB - PC Ha: Not all population proportions are equal. (b) Using a 0.05 level of significance, conduct the hypothesis test. Find the value of the test statistic. (Round your answer to three decimal places.) Find the p-value. (Round your answer to four decimal places.) p-value = State vour conclusion.O Reject Ho. We cannot conclude that the suppliers do not provide equal proportions of defective components. O Do not reject Ho. We cannot conclude that the suppliers do not provide equal proportions of defective components. Reject Ho. We conclude that the suppliers do not provide equal proportions of defective components. O Do not reject Ho- We conclude that the suppliers do not provide equal proportions of defective components. (c) Conduct a multiple comparison test to determine if there is an overall best supplier or if one supplier can be eliminated because of poor quality. Use a 0.05 level of significance. (Round your answers for the critical values to four decimal places. Comparison Significant CVu Diff > CVij A VS. B A vs. C B VS. C Can any suppliers be eliminated because of poor quality? (Select all that apply.) Supplier A O Supplier B O Supplier C none DETAILS MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER A chi-square significance test is performed to exam between two categorical variables in a 8 x 6 table. What are the degrees of freedom associated with the test statistic? 4. DETAILS PREVIOUS ANSWERS MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER In economic downturns or to improve their competitiveness, corporations may undertake a "reduction in force" (RIF), where substantial numbers of employees are released. Federal and state laws require that employees be treated equally regardless of their age. In particular, employees over the age of 40 years are a "protected class." Many allegations of discrimination focus on comparing employees over 40 with their younger coworkers. Here are the data for a recent RIF. Over 40 Released No Yes Yes 8 40 No 503 766 (a) Complete this two-way table by adding marginal and table totals. Over 40 Released No Yes Totals Yes 7 44 No 504 762 Totals What percent of each employee age group (over 40 or not) were released? Under 40, Over 40, % joes there appear to be a relationship between age and being released? O yes no (b) Perform the chi-square test. Give the test statistic, the degrees of freedom, the P-value, and your conclusion. x2 = df = P-value = Conclusion Reject H. There is evidence that there is a relationship between employee's age and being released. O Do not reject H. There is evidence that there is a re employee's age and being released. O Reject Ho. There is no evidence that there is a relationship between employee's age and being released Do not reject Ho. There is no evidence that there is a relationship between employee's age and being released.DETAILS PREVIOUS ANSWERS MY NOTES ASK YOUR TEACHER DATAfile: WorkforcePlan You may need to use the appropriate technology to answer this question. A Deloitte employment survey asked a sample of human resource executives how their company planned to change its workforce over the next 12 months. A categorical response variable showed three options: the company plans to hire and add to the number of employees, the company plans no change in the number of employees, or the company plans to lay off and reduce the number of employees. Another categorical variable indicated if the company was private or public. Sample data for 180 companies are summarized as follows. Company Employment Plan Private | Public Add Employees 37 32 No Change 19 34 Lay Off Employees 16 42 (a) Conduct a test of independence to determine if the employment plan for the next 12 months is independent of the type of company. State the null and alternative hypotheses O Ho: Employment plan is mutually exclusive from the type of company. He: Employment plan is not mutually exclusive from the type of company. Ho: Employment plan is independent of the type of company. He: Employment dent of the type of company. O Ho: Employment plan is not independent of the type of company. He: Employment plan is independent of the type of company. He: Employment plan is not mutually exclusive from the type of company. He: Employment plan is mutually exclusive from the type of company. Find the value of the test statistic. (Round your answer to three decimal places.) Find the p-value. (Round your answer to four decimal places.) p-value =[ 6. DETAILS PREVIOUS ANSWERS MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER You may need to use the appropriate technology to answer this question. A survey was conducted to determine whether hours of sleep per night are independent of age. A sample of individuals was asked to indicate the number of hours of sleep per night with categorical options: fewer than 6 hours, 6 to 6.9 hours, 7 to 7.9 hours, and 8 hours or more. Later in the survey, the individuals were asked to indicate their age with categorical options: age 39 or younger and age 40 or older. Sample data follow. Age Group Hours of Sleep 39 or younger |40 or older Fewer than 6 38 36 6 to 6.9 60 57 7 to 7.9 77 75 8 or more 65 92 (a) Conduct a test of independence to determine whether hours of sleep are independent of age. State the null and alternative hypotheses O Ho: Hours of sleep per night is mutually exclusive from age. Ha: Hours of sleep per night is not mutually exclusive from age. D He: Hours of sleep per night is not independent of age He: Hours of sleep per night is independent of age. Ho: The proportion of people who get 8 or more hours of sleep per night is not equal across the two age groups. He: The proportion of people who get 8 or more hours of sleep per night is equal across the two age groups. O Ho: Hours of sleep per night is independent of age H : Hours of sleep per night is not independent of age. Find the value of the test statistic. (Round your answer to three decimal places.) what is the p-value? (Round your answer to four decimal places.) p-value = (b) What is your estimate of the percentages of individuals who sleep fewer than 6 hours, 6 to 6.9 hours, 7 to 7.9 hours, and 8 hours or more per night? Fewer than 6 6 to 6.9 7 to 7.9 8 or more7 DETAILS PREVIOUS ANSWERS MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER You may need to use the appropriate technology to answer this question. Test the following hypotheses by using the y goodness of fit test. Hoi PA = 0.40, Pa = 0.40, and pc = 0.20 H : The population proportions are not p, = 0.40, Pg = 0.40, and Pe = 0.20. A sample of size 200 yielded 140 in category A, 20 in category B, and 40 in category C. Use a = 0.01 and test to see whether the proportions are as stated in Ho (a) Use the p-value approach. Find the value of the test statistic. Find the p-value. (Round your answer to four decimal places.) p-value - State your conclusion. Reject H . We conclude that the proportions differ from 0.40, 0.40, and 0.20. O Do not reject H . We cannot conclude that the proportions are equal to 0.40, 0.40, and 0.20. O Do not reject Ho. We cannot conclude that the proportions differ from 0.40, 0.40, and 0.20. O Reject Ho. We conclude that the proportions are equal to 0.40, 0.40, and 0.20. (b) Repeat the test using the critical value approach. Find the value of the test statistic. State the critical values for the rejection rule. (If the test is one-tailed, enter NONE for the unused tail. Round your answers to three decimal places.) test statistic s test statistic 2DETAILS PREVIOUS ANSWERS MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER You may need to use the appropriate technology to answer this question. The National Highway Traffic Safety Administration reported the percentage of traffic accidents occurring each day of the week. Assume that a sample of 420 accidents provided the following data. Sunday Monday y Tuesday | Wednesday |Thursday | Friday Saturday 66 50 53 47 55 69 80 (a) Conduct a hypothesis test to determine if the proportion of traffic accidents is the same for each day of the week. Use a 0.05 level of significance. State the null and alternative hypotheses. Ho: Psun = PMon = PTue = Pwed = PThu = PFri = Psat = H: Not all proportions are equal. O Ho: Psun # PMan # PTUE * Pwed * Pru # PFri * Psat # 7 He : All proportions are equal. O Ho: Not all proportions are equal. Hai Psun * PMon * PTUC * Pwed # PThu * Pen + Psat #7 O Ho: Not all proportions are equal. He: Psun = PMen = PTue = Pwed = PThu = Ppri = Psat = 7 Find the value of the test statistic. (Round your answer to three decimal places.) Find the p-value. (Round your answer to four decimal places.) p-value = State your conclusion. " Reject Ha. We conclude that the proportion of traffic accidents is not the same for each day of the week. Do not reject Ho. We conclude that the proportion of traffic a accidents is the same for each day of the week. Reject My. We conclude that the proportion of traffic accidents is the same for each day of the week. (b) Compute the percentage of traffic accidents occurring on each day of the week. (Round your answers to two decimal places.) Sunday 1% Monday % Tuesday % Wednesday Thursday Friday Saturday 1% What day has the highest percentage of traffic accidents? O Sunday O Monday O Tuesday O Wednesday O Thursday O Friday O Saturday
