MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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Question

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

Regression model The regression equation for ANOVA is given by y = Bo + B₁ + region South + B + regionWest + where ~ N(0,0²). The dummy variables regionSouth and regionWest are created by the 1m () function and appear in the output below. Fitting the ANOVA model and output from summary() and anova () functions The following R code fit the ANOVA model with 1m () function and print outputs from summary() function and anova () function. anov_out <- lm (balance - region, data = dat) summary (anov_out) ** ## Call: ## 1m (formula = balance - region, data = dat) ## Residuals: Min 1Q Median 3Q Max ## -531.00 -457.08 -63.25 339.25 1480.50 ## Coefficients: ## ## (Intercept) ## regionSouth -12.50 ## regionWest -18.69 Estimate Std. Error t value Pr(>1t|) 531.00 46.32 11.464 <2e-16 *** 56.68 -0.221 65.02 -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: 0.9575 anova (anov_out) ## Analysis of Variance Table ## Box plot 0.826 0.774 Df 2 ## region ## Residuals 397 84321458 212397 Sum Sq Mean Sq F value Pr(>F) 18454 9227 0.0434 0.9575 boxplot (balance - region, data = dat)
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Transcribed Image Text:Regression model The regression equation for ANOVA is given by y = Bo + B₁ + region South + B + regionWest + where ~ N(0,0²). The dummy variables regionSouth and regionWest are created by the 1m () function and appear in the output below. Fitting the ANOVA model and output from summary() and anova () functions The following R code fit the ANOVA model with 1m () function and print outputs from summary() function and anova () function. anov_out <- lm (balance - region, data = dat) summary (anov_out) ** ## Call: ## 1m (formula = balance - region, data = dat) ## Residuals: Min 1Q Median 3Q Max ## -531.00 -457.08 -63.25 339.25 1480.50 ## Coefficients: ## ## (Intercept) ## regionSouth -12.50 ## regionWest -18.69 Estimate Std. Error t value Pr(>1t|) 531.00 46.32 11.464 <2e-16 *** 56.68 -0.221 65.02 -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: 0.9575 anova (anov_out) ## Analysis of Variance Table ## Box plot 0.826 0.774 Df 2 ## region ## Residuals 397 84321458 212397 Sum Sq Mean Sq F value Pr(>F) 18454 9227 0.0434 0.9575 boxplot (balance - region, data = dat)
500 1000 1500 2000 balance 0 East O South region West We 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 $. The mean balance for East, South and West are denoted, respectively, by 1, 2 and 3. Data set library (ISLR2) head (Credit) 2 34 11 No 3 82 15 Yes ## Income Limit Rating Cards Age Education Own Student Married Region Balance ## 1 14.891 3606 ## 2 106.025 6645 ## 3 104.593 7075 ## 4 148.924 9504 ## 5 55.882 4897 ## 6 80.180 8047 4 71 3 36 2 68 4 77 Yes South Yes West No West No West Yes South No South 283 483 514 681 357 569 balance <- Credit$Balance region <as.factor (Credit$Region) dat <- data.frame (region, balance) str(dat) ## region ## East 99 ## South: 199 ## West 102 ## ## ## 11 No 11 Yes. balance : Min. 1st Qu.: Median Mean 3rd Qu.: 863.00 0.00 68.75 459.50 : 520.01 Max. :1999.00 16 No 10 No ## 'data.frame': 400 obs. of 2 variables: ## $ region Factor w/ 3 levels "East", "South",..: 2 3 3 3 2 2 1 3 2 1 ... ## $ balance: num 333 903 580 964 331 summary (dat) No Yes No No No No 333 903 580 964 331 1151
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Transcribed Image Text:500 1000 1500 2000 balance 0 East O South region West We 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 $. The mean balance for East, South and West are denoted, respectively, by 1, 2 and 3. Data set library (ISLR2) head (Credit) 2 34 11 No 3 82 15 Yes ## Income Limit Rating Cards Age Education Own Student Married Region Balance ## 1 14.891 3606 ## 2 106.025 6645 ## 3 104.593 7075 ## 4 148.924 9504 ## 5 55.882 4897 ## 6 80.180 8047 4 71 3 36 2 68 4 77 Yes South Yes West No West No West Yes South No South 283 483 514 681 357 569 balance <- Credit$Balance region <as.factor (Credit$Region) dat <- data.frame (region, balance) str(dat) ## region ## East 99 ## South: 199 ## West 102 ## ## ## 11 No 11 Yes. balance : Min. 1st Qu.: Median Mean 3rd Qu.: 863.00 0.00 68.75 459.50 : 520.01 Max. :1999.00 16 No 10 No ## 'data.frame': 400 obs. of 2 variables: ## $ region Factor w/ 3 levels "East", "South",..: 2 3 3 3 2 2 1 3 2 1 ... ## $ balance: num 333 903 580 964 331 summary (dat) No Yes No No No No 333 903 580 964 331 1151
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