Employees of a state university system can choose from among four different health plans. Each plan differs somewhat from the others in terms of hospitalization coverage. Four random samples of recently hospitalized individuals were selected, each sample consisting of people covered by a different health plan. The length of the hospital stay (number of days) was determined for each individual selected. LUSE SALT (a) What hypotheses would you test to decide whether the mean lengths of stay are not the same for all four health plans? (Let ₁ 2 3, and 4 be the true mean length of hospital stay for the four differe health plans.) OH₂H₁ = ₂ = 3 = 14 H: all four of the 's are different O Ho H1 H₂ H3* H4 Ha: at least one pair of the four μ's are the same Ho H₁ H₂ H3 = 14 H: at least one pair of the four μ's are different O Ho: all four of the 's are different H₂H₁=₂=H3 = H4 OHO: at least one pair of the four μ's are different H₂H₁ = ₂ = 3 = μ4 (b) If each sample consisted of seven individuals and the value of the ANOVA F statistic was F = 4.27. What can be said about the P-value for this test? OP-value > 0.100 O 0.050 < P-value < 0.100 O 0.010 < P-value < 0.050 0.001 < P-value < 0.010 OP-value < 0.001 What conclusion would be appropriate for a test with a = 0.01? O Fail to reject Ho. There is not convincing evidence that the mean length of hospital stay is not the same for all four health plans. O Reject Ho. There is convincing evidence that the mean length of hospital stay is not the same for all four health plans. O Reject Ho. There is not convincing evidence that the mean length of hospital stay is not the same for all four health plans. O Fail to reject Ho. There is convincing evidence that the mean length of hospital stay is not the same for all four health plans. (c) Answer the question posed in part (b) if the F value given there resulted from sample sizes n₁ = 8, n₂ = 7, n3 = 7, and n₁ = 6. What can be said about the P-value for this test? OP-value > 0.100 O 0.050 P-value < 0.100 O 0.010 P-value < 0.050 O 0.001 < P-value < 0.010 OP-value < 0.001 The conclusion is the following. O Reject Ho. There is convincing evidence that the mean length of hospital stay is not the same for all four health plans. O Reject Ho. There is not convincing evidence that the mean length of hospital stay is not the same for all four health plans. O Fail to reject Ho. There is convincing evidence that the mean length of hospital stay is not the same for all four health plans. O Fail to reject Ho. There is not convincing evidence that the mean length of hospital stay is not the same for all four health plans.