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If X1, X2, ...Xn is a random sample from N(0, σ^2), How would you show the following?
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- The results of an independent-measures research study are reported as "t(20) = 2.12, p < .05, two tails." For this study, what t values formed the boundaries for the critical region?The result of an idependent measures study reports as t(22)=2.12p<.05, two tails. For this study, what t values formed the boundaries for the critical region? Note: Make sure that you include the+- sign to your answer.At α-value=0.01, test whether there is a significant relationship between thedependent variable (Y) and the independent variables (X1, X2 and X3).
- Find the local linearization of f(x) = x² at –3. %3D L_3(x) =Data on alcohol content and wine quality was collected from variants of a particular wine. From a sample of 46 wines, a model was created using the percentages of aloohol to predict wine quality Y-0.337 +0.5635X,, where X, in the alcohol content (%) and Y, is the rated quality of the wine. For these data, Syx 0.9316, X 10.63, and h 0.027260 when X 10. Complete parta (a) throi a. Construct a 05% confidence interval estimate of the mean wine quality rating for all wines that have 10% alcohol. 4.988 spypx= 10 s 5.608 (Type integers or decimals. Round to three decimal places as needed. Use ascending order) b. Construct a 95% prediction interval of the wine quality rating of an individual wine that has 10% alcohol. (Type integers or decimals. Round to three decimal places as needed. Use ascending order.)Q/Fit (y = ax² + (b/x)) to the following data: (x:1, 2, 3, 4), (y: -1.51, 0.99, 3.88, 7.66). *
- 8. Identify all critical points of f(x, y) = 6xy-x - y? and classify each as an appropriate relative extrema or a saddle point. %3DWe have seen that two different tests for Ho B₁ = 0 versus H₁: B₁0, a t-test and a F-test. : Please show that the F-test statistic is equal to the t-test statistic squared. Hint: F-test statistic = t-test statistic MSreg MSres B₁ s.e.(B₁) " where M.Sreg = ₁(Ŷ₁ – Ý)², MSres = Σ₁₁ (Y₁ – Ŷ₁)²/(n − 2). - =1Could you help me calculate r? Also could you demonstrate how to find the critical value?
- Compute the average value of f(x) Average value = = X 1 4x + 3 on the interval [2,6].Determine the critical value z a/2Samples of 2 units will be selected from the population whose distribution is given below, with a return and order of importance (W / R, O / I). a)Show that x̄ is a neutral estimator. b)Find V(x̄). Show that V(x̄) is equals to ϭ²/n. c)Find E(s²). Show that E(s²) is equal to ϭ². (Hint: W/R=With Replacement, O/I=Order Important)