Test the claim about the difference between two population means μ₁ and ₂ at the level of significance x. Assume the samples are random and independent, and the populations are normally distributed. Claim: μ₁ μ₂; α=0.01. Assume o² #02 Sample statistics: x₁=2413, S₁ = 176, n₁ = 12 and x2 =2294, s₂ = 54, n₂ = 11 Identify the null and alternative hypotheses. Choose the correct answer below. OA. Ho: H₁ H₂ Hai HSH2 OC. Ho: H₁ H₂ Ha: H1 H₂ OE. Ho: H₁ H₂ Hai HH2 Find the standardized test statistic t. t= (Round to two decimal places as needed.) Find the P-value. Fail to reject OB. Ho: H₁ H₂ Hai H2H2 Reject OD. Hoi Hy #U2 Ha: H1 H₂ P= (Round to three decimal places as needed.) Decide whether to reject or fail to reject the null hypothesis and interpret the decision in the context of the original claim. Ho. There enough evidence at the 1% level of significance to reject the claim. OF. Ho: H₁ H2 Hai Hy H2

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