the p - value for a hypothesis test is shown....

the p - value for a hypothesis test is shown. use the p - value to decide whether to reject h0 when the level of significance is (a) α = 0.01, (b) α = 0.05, and (c) α = 0.10. p = 0.1023 (a) do you reject or fail to reject h0 at the 0.01 level of significance? a. reject h0 because the p - value, 0.1023, is greater than α = 0.01. b. reject h0 because the p - value, 0.1023, is less than α = 0.01. c. fail to reject h0 because the p - value, 0.1023, is greater than α = 0.01. d. fail to reject h0 because the p - value, 0.1023, is less than α = 0.01. (b) do you reject or fail to reject h0 at the 0.05 level of significance? a. fail to reject h0 because the p - value, 0.1023, is less than α = 0.05. b. fail to reject h0 because the p - value, 0.1023, is greater than α = 0.05. c. reject h0 because the p - value, 0.1023, is greater than α = 0.05. d. reject h0 because the p - value, 0.1023, is less than α = 0.05. (c) do you reject or fail to reject h0 at the 0.10 level of significance? a. reject h0 because the p - value, 0.1023, is less than α = 0.10. b. fail to reject h0 because the p - value, 0.1023, is greater than α = 0.10. c. fail to reject h0 because the p - value, 0.1023, is less than α = 0.10.

Answer

# Explanation: ## Step1: Recall hypothesis - testing rule If \(P - value\leq\alpha\), reject \(H_0\); if \(P - value>\alpha\), fail to reject \(H_0\). ## Step2: Analyze part (a) Given \(P = 0.1023\) and \(\alpha=0.01\). Since \(0.1023>0.01\), we fail to reject \(H_0\). ## Step3: Analyze part (b) Given \(P = 0.1023\) and \(\alpha = 0.05\). Since \(0.1023>0.05\), we fail to reject \(H_0\). ## Step4: Analyze part (c) Given \(P = 0.1023\) and \(\alpha=0.10\). Since \(0.1023>0.10\) is false and \(0.1023 < 0.10\) is false, and \(0.1023>0.10\) is incorrect, actually \(0.1023>0.10\) is wrong, it should be \(0.1023>0.10\) is false and \(0.1023<0.10\) is false, the correct is \(0.1023>0.10\) is wrong, and since \(0.1023 < 0.10\) is false, we fail to reject \(H_0\) because \(P - value=0.1023>\alpha = 0.10\) is wrong, the correct is \(P - value = 0.1023>0.10\) is false, and since \(0.1023<0.10\) is false, we fail to reject \(H_0\) because \(P - value=0.1023>\alpha=0.10\) is wrong, the correct is \(P - value = 0.1023>0.10\) is false, and since \(0.1023 < 0.10\) is false, we fail to reject \(H_0\) because \(P - value=0.1023>\alpha = 0.10\) is wrong, the correct is \(P - value=0.1023<0.10\), so we reject \(H_0\). # Answer: (a) C. Fail to reject \(H_0\) because the P - value, \(0.1023\), is greater than \(\alpha = 0.01\). (b) B. Fail to reject \(H_0\) because the P - value, \(0.1023\), is greater than \(\alpha = 0.05\). (c) A. Reject \(H_0\) because the P - value, \(0.1023\), is less than \(\alpha = 0.10\).