You may need to use the appropriate technology to answer this question. A certain manufacturer is a producer of aluminum components for the avionics and automotive industries. At its plant, an...

Extracted text: You may need to use the appropriate technology to answer this question. A certain manufacturer is a producer of aluminum components for the avionics and automotive industries. At its plant, an engineer has conducted a quality-control test in which aluminum coils produced in all three shifts were inspected. The study was designed to determine if the population proportion of good parts was the same for all three shifts. Sample data follow. Production Shift Quality First second Third Good 282 364 172 Defective 18 36 28 (a) Using a 0.05 level of significance, conduct a hypothesis test to determine if the population proportion of good parts is the same for all three shifts. State the null and alternative hypotheses. O Hại Not all population proportions are equal. H:P, - P, = P3 O Ho: At least two population proportions are equal. Ha: P1* P2" P3 O Hgi P, * P2* P3 H: All population proportions are equal. O Hoi P, - P2 "P3 H: Not all population proportions are equal. 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 Hg. We conclude the population proportion of good parts is not equal for all three shifts. O Reject Hg. We conclude the population proportion of good parts is equal for all three shifts. O Do not reject Hg. We conclude the population proportion of good parts is equal for all three shifts. O Do not reject H. We conclude the population proportion of good parts is not equal for all three shifts. (b) If the conclusion is that the population proportions are not all equal, use a multiple comparison procedure to determine how the shifts differ in terms of quality. Which shifts differ significantly? (Select all that apply.) O shift 1 vs. shift 2 O shift 1 vs. shift 3 shift 2 vs. shift 3 O None differ significantly. What shift or shifts need to improve the quality of parts produced? Shift 1, because it differs significantly from shift 3. O Shift 3, because it differs significantly from shift 1. O Shifts 1 and 2, because they differ significantly from shift 3. O Shifts 2 and 3, because they differ significantly from shift 1. O No shifts need to improve, because no shift differs significantly from either of the others.