(Solution) - Alice did a two sample t test of the hypotheses H0 1 -(2025 Original AI-Free Solution)

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Alice did a two-sample t test of the hypotheses H0:µ1 = µ2 versus HA: µ1 ? µ2, using samples sizes of n1 = n2 = 15. The P-value for the test was 0.13, and ? was (1.10. It happened that 1 was less than 2. Unbeknownst to Alice, Linda was interested in the same data. However, Linda had reason to believe, based on an earlier study of which Alice was not aware, that either µ1 = µ2 or else µ1 < µ2. Thus, Linda did a test of the hypotheses H0. µ1 = µ2 versus HA: µ1 < µ2. So, for Linda's test
(i) The P-value would still be 0.13 and H0 would not be rejected if ? = 0.10.
(ii) The P-value would still be 0.13 and H0 would be rejected if ? = 0.10.
(iii) The P-value would be less than 0.13 and H0 would not be rejected if ? = 0.10.
(iv) The P-value would be less than 0.13 and H0 would be rejected if ? = 0.10.
(v) The P-value would be greater than 0.13 and H0 would not be rejected if ? = 0.10.
(vi) The P-value would be greater than 0.13 and H0 would be rejected if ? = 0.10.
Choose one of these and briefly explain why your choice is true.