Q2 ANOVA The following side-by-side box plots show the prices (in thousands) of 48 houses in Corvallis, OR. The houses are divided into age categories: N = New (0-24 years old), M = Medium (25-50 years old), O = Old (50-75 years old), and VO = Very Old (75+ years old). Each category contains 12 randomly selected homes. 500 - 400 - 300 - House Price in Thousands 200 - 100 - M N o vo Age Category Q2.1 TRUE or FALSE: All categories contain at least one outlier. O True O FalseQ2.2 TRUE or FALSE: The median house price for each category is less than $400,000. O True O False Q2.3 State the alternative hypothesis used to test whether there is a difference in average house price for the four age categories. O The average house price for each age category is equal to O. O All of the average house prices for the four age categories differ from one another. O At least two age categories differ in average house price. O The average house prices for all four age categories are equal. Q2.4 Below is the R output for the ANOVA F test. of Sum Sq Mean Sq F value Pr (>F) `Age Category" 3 20649 6883 0. 423 Residuals 44 317444 7215 The average variation between age categories isG2i Elelovur is the F! output for the ANDUA F test. Df Sum Sq Mean Sq F value Pr[}F) 'Age Category' 3 20649 6883 0.423 Residuals 44 311444 7215 The F statistic for the snow. F test is G2i Based on the F test statistic and pvalue from the SingleFactor ANDUA table, indicate whether the statement is a TRUE or FALSE conclusion of the test. There is convincing evidence the overoge house prices of the four oge categories ore different. 0 True 0 False Q2.7 Based on the F test statistic and p-value from the Single-Factor ANOVA table, indicate whether the statement is a TRUE or FALSE conclusion of the test. We will fail to reject the null hypothesis that the average house prices for the four age categories are different at the 0.1 significance level. O True O False Q2.8 Based on the F test statistic and p-value from the Single-Factor ANOVA table, indicate whether the statement is a TRUE or FALSE conclusion of the test. We should perform a multiple comparisons procedure to see which means differ from each other. O True O False