We wish to test of hypothesisH0 : μ1 = μ2 = μ3vsH1 : Not all group means are the same.Use the significance level α = 0.01.a. Find the value of the test statistic and its distribution.b. Find the rejection region.c. Find the p-value of the test.d. Make a conclusionall subparts please! thank you Regression modelThe regression equation for ANOVA is given byy = Bo + B₁ + region South + B + regionWest +where ~ N(0,0²). The dummy variables regionSouth and regionWest are created by the 1m () functionand appear in the output below.Fitting the ANOVA model and output from summary() and anova () functionsThe following R code fit the ANOVA model with 1m () function and print outputs from summary() functionand anova () function.anov_out <- lm (balance - region, data = dat)summary (anov_out)**## Call:## 1m (formula = balance - region, data = dat)## Residuals:Min1Q Median3QMax## -531.00 -457.08 -63.25 339.25 1480.50## Coefficients:#### (Intercept)## regionSouth -12.50## regionWest -18.69Estimate Std. Error t value Pr(>1t|)531.0046.32 11.464 <2e-16 ***56.68 -0.22165.02 -0.287## Signif. codes: 0*** 0.001 0.01 0.05 0.11#### Response: balance#### Residual standard error: 460.9 on 397 degrees of freedom## Multiple R-squared: 0.0002188, Adjusted R-squared: -0.004818## F-statistic: 0.04344 on 2 and 397 DF, p-value: 0.9575anova (anov_out)## Analysis of Variance Table##Box plot0.8260.774Df2## region## Residuals 397 84321458 212397Sum Sq Mean Sq F value Pr(>F)18454 9227 0.0434 0.9575boxplot (balance - region, data = dat) 500 1000 1500 2000balance0EastOSouthregionWestWe wish to compare Balance in 3 different Region.• Region: A factor with levels East, South, and West indicating the individual's geographical location.Balance: Average credit card balance in $.The mean balance for East, South and West are denoted, respectively, by 1, 2 and 3.Data setlibrary (ISLR2)head (Credit)2 3411 No3 8215 Yes## Income Limit Rating Cards Age Education Own Student Married Region Balance## 1 14.891 3606## 2 106.025 6645## 3 104.593 7075## 4 148.924 9504## 5 55.882 4897## 6 80.180 80474 713 362 684 77Yes SouthYesWestNo WestNo WestYes SouthNo South283483514681357569balance <- Credit$Balanceregion

Given information:k= 3 Groups n= 400 Total observation Inference One way ANOVA

We wish to test of hypothesis H0 : μ1 = μ2 = μ3 vs H1 : Not all group means are the same. Use the significance level α = 0.01. a. Find the value of the test statistic and its distribution. b. Find the rejection region. c. Find the p-value of the test. d. Make a conclusion all subparts please! thank you

We wish to test of hypothesis H0 : μ1 = μ2 = μ3 vs H1 : Not all group means are the same. Use the significance level α = 0.01. a. Find the value of the test statistic and its distribution. b. Find the rejection region. c. Find the p-value of the test. d. Make a conclusion all subparts please! thank you

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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