Question
Had to post a new photo. I couldn't edit from my phone
This Test: 1 An insurance agent randomly selected 10 of his Variable Count Mean StdDev clients and checked online price quotes for their Local 10 949.900 303.894 policies. His summaries of the data are shown, Online 10 901.300 285.884 where Diff is Local-Online. Diff 10 48.6000 159.927 Test an appropriate hypothesis to see if there is evidence that drivers might save money by switching to an online agent. Use a 0.05. Ea Click here to view the insurance quote data. O D. H da 0 Are the conditions for matched pairs inference satisfied? Select all that apply. A. No.It cannot be determined if the Independence Assumption is satisfied. B. Yes, all three conditions for mached pairs inference are satisfied C. No, the Nearly Normal Condition is not satisfied. O D. No, the Independence Assumption is not satisfied. E. No, the Paired Data Condition is not satisfied. Compute the test statistic. The test statistic is (Round to two decimal places as needed.) Find the P-value. The P-value is (Round to three decimal places as needed.) Determine the appropriate conclusion. Choose the correct answer below. O A. Fail to reject Hn. There is insufficient evidence that drivers would save monev bv switchina. Click to select your answer(s).
Explanation / Answer
Expanding (X-a)2 = X^2 +a^2 -2Xa, in the below formula:
E[(X-a)2] = E(X^2) +E(a^2) + E(-2aX)............0
E(a^2) = a^2
E(-2aX) = -2aE(X) = -2aµ
Now, Var(X) = E(X^2)-E(X)^2
2 +µ2 = E(X^2)
E(X^2) =2 -µ2.......subbing in the equation 0 , we have:
E[(X a)2] = 2 +µ2+ a^2 - 2aµ
=2 + ( µ2+ a^2 - 2aµ)
=2 + ( µ-a)2
Hence Proved
