Exam 11: Experimental Design and Analysis of Variance

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Find an individual 95 percent confidence interval for Find an individual 95 percent confidence interval for   where   <sub>1</sub> = 33.98,   <sub>2</sub> = 36.56,and MSE = 0.669.There were 15 observations total and 3 treatments.Assume that the number of observations in each treatment is equal. where Find an individual 95 percent confidence interval for   where   <sub>1</sub> = 33.98,   <sub>2</sub> = 36.56,and MSE = 0.669.There were 15 observations total and 3 treatments.Assume that the number of observations in each treatment is equal. 1 = 33.98, Find an individual 95 percent confidence interval for   where   <sub>1</sub> = 33.98,   <sub>2</sub> = 36.56,and MSE = 0.669.There were 15 observations total and 3 treatments.Assume that the number of observations in each treatment is equal. 2 = 36.56,and MSE = 0.669.There were 15 observations total and 3 treatments.Assume that the number of observations in each treatment is equal.

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Consider the following partial analysis of variance table from a randomized block design with 10 blocks and 6 treatments. Consider the following partial analysis of variance table from a randomized block design with 10 blocks and 6 treatments.   Test H<sub>o</sub>: there is no difference between treatment effects at   = .05. Test Ho: there is no difference between treatment effects at Consider the following partial analysis of variance table from a randomized block design with 10 blocks and 6 treatments.   Test H<sub>o</sub>: there is no difference between treatment effects at   = .05. = .05.

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A company that fills gallon containers of water has four machines.The quality control manager needs to determine whether the average fill for these machines is the same.Looking at 19 gallon containers we have the following data of fill measures in quarts: A company that fills gallon containers of water has four machines.The quality control manager needs to determine whether the average fill for these machines is the same.Looking at 19 gallon containers we have the following data of fill measures in quarts:   and the following partial ANOVA table:   Determine the degrees of freedom for the treatment,error,and total and state the critical value of the F statistic at   = .05. and the following partial ANOVA table: A company that fills gallon containers of water has four machines.The quality control manager needs to determine whether the average fill for these machines is the same.Looking at 19 gallon containers we have the following data of fill measures in quarts:   and the following partial ANOVA table:   Determine the degrees of freedom for the treatment,error,and total and state the critical value of the F statistic at   = .05. Determine the degrees of freedom for the treatment,error,and total and state the critical value of the F statistic at A company that fills gallon containers of water has four machines.The quality control manager needs to determine whether the average fill for these machines is the same.Looking at 19 gallon containers we have the following data of fill measures in quarts:   and the following partial ANOVA table:   Determine the degrees of freedom for the treatment,error,and total and state the critical value of the F statistic at   = .05. = .05.

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Different levels of a factor are called

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A company that fills gallon containers of water has four machines.The quality control manager needs to determine whether the average fill for these machines is the same.Looking at 19 gallon containers we have the following data of fill measures in quarts: A company that fills gallon containers of water has four machines.The quality control manager needs to determine whether the average fill for these machines is the same.Looking at 19 gallon containers we have the following data of fill measures in quarts:   and the following partial ANOVA table:   Complete the ANOVA table and calculate and the following partial ANOVA table: A company that fills gallon containers of water has four machines.The quality control manager needs to determine whether the average fill for these machines is the same.Looking at 19 gallon containers we have the following data of fill measures in quarts:   and the following partial ANOVA table:   Complete the ANOVA table and calculate Complete the ANOVA table and calculate

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Consider the following partial analysis of variance table from a randomized block design with 6 blocks and 4 treatments. Consider the following partial analysis of variance table from a randomized block design with 6 blocks and 4 treatments.   What is the mean square error? What is the mean square error?

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Consider the following calculations for a one-way analysis of variance from a completely randomized design with 20 total observations. MSE = 101.25 Consider the following calculations for a one-way analysis of variance from a completely randomized design with 20 total observations. MSE = 101.25   <sub>overall</sub> = 39   <sub>1</sub> = 33   <sub>2</sub> = 43   <sub>3</sub> = 49   <sub>4</sub> = 31 Compute a 95% confidence interval for the second treatment mean. overall = 39 Consider the following calculations for a one-way analysis of variance from a completely randomized design with 20 total observations. MSE = 101.25   <sub>overall</sub> = 39   <sub>1</sub> = 33   <sub>2</sub> = 43   <sub>3</sub> = 49   <sub>4</sub> = 31 Compute a 95% confidence interval for the second treatment mean. 1 = 33 Consider the following calculations for a one-way analysis of variance from a completely randomized design with 20 total observations. MSE = 101.25   <sub>overall</sub> = 39   <sub>1</sub> = 33   <sub>2</sub> = 43   <sub>3</sub> = 49   <sub>4</sub> = 31 Compute a 95% confidence interval for the second treatment mean. 2 = 43 Consider the following calculations for a one-way analysis of variance from a completely randomized design with 20 total observations. MSE = 101.25   <sub>overall</sub> = 39   <sub>1</sub> = 33   <sub>2</sub> = 43   <sub>3</sub> = 49   <sub>4</sub> = 31 Compute a 95% confidence interval for the second treatment mean. 3 = 49 Consider the following calculations for a one-way analysis of variance from a completely randomized design with 20 total observations. MSE = 101.25   <sub>overall</sub> = 39   <sub>1</sub> = 33   <sub>2</sub> = 43   <sub>3</sub> = 49   <sub>4</sub> = 31 Compute a 95% confidence interval for the second treatment mean. 4 = 31 Compute a 95% confidence interval for the second treatment mean.

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_____ simultaneous confidence intervals test all of the pairwise differences between means respectively while controlling the overall Type I error.

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Consider the following partial analysis of variance table from a randomized block design with 6 blocks and 4 treatments. Consider the following partial analysis of variance table from a randomized block design with 6 blocks and 4 treatments.   Determine the degrees of freedom for error. Determine the degrees of freedom for error.

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A company that fills gallon containers of water has four machines.The quality control manager needs to determine whether the average fill for these machines is the same.Looking at 19 gallon containers we have the following data of fill measures in quarts:  A company that fills gallon containers of water has four machines.The quality control manager needs to determine whether the average fill for these machines is the same.Looking at 19 gallon containers we have the following data of fill measures in quarts:    and the following partial ANOVA table:    Is there a significant difference in the fill amounts of the four machines at  \alpha  = .05 to reject the null hypothesis? and the following partial ANOVA table:  A company that fills gallon containers of water has four machines.The quality control manager needs to determine whether the average fill for these machines is the same.Looking at 19 gallon containers we have the following data of fill measures in quarts:    and the following partial ANOVA table:    Is there a significant difference in the fill amounts of the four machines at  \alpha  = .05 to reject the null hypothesis? Is there a significant difference in the fill amounts of the four machines at α\alpha = .05 to reject the null hypothesis?

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The error sum of squares measures the between-treatment variability.

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In a completely randomized (one-way)analysis of variance problem with c groups and a total of n observations in all groups,the variance between groups is equal to:

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Consider the following partial analysis of variance table from a randomized block design with 6 blocks and 4 treatments. Consider the following partial analysis of variance table from a randomized block design with 6 blocks and 4 treatments.   Determine the degrees of freedom for treatments. Determine the degrees of freedom for treatments.

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We have just performed a one-way ANOVA on a given set of data and rejected the null hypothesis for the ANOVA F test.Assume that we are able to perform a randomized block design ANOVA on the same data.For the randomized block design ANOVA,the null hypothesis for equal treatments will ______ be rejected.

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After analyzing a data set using one-way ANOVA model,the same data is analyzed using the randomized block design ANOVA model.SS (Treatment)in the one way ANOVA model is _______________ the SS (Treatment)in the randomized block design ANOVA model.

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