Figure 2 shows the results of the Tukey test to test pairwise differences at the significance level 0.05 for the additive model using design and region with regards to their impact on the survey responses. Figure 2. (1st Image uploaded below) Tukey test results showing pairwise factor level comparison with regards to impact on the survey responses. P adj shows the p value for each pairwise level comparison. P values with 0.0000000 indicate that the p value is < 0.00000001. Considering a significance level of alpha = 0.05, select the correct statement below. A.) For region, all pairwise Region levels differ from each other significantly with regards to survey responses. B.) For design, all pairwise Design levels differ from each other significantly with regards to survey responses. C.) The average survey response using Design 3 is 175.58 higher than the average survey response using Design 2. D.) Designs 1 and 3 do not differ significantly; but Design 2 is significantly different than Design 1, and Design 2 is significantly different than Design 3 with regards to survey responses. 2. Use the following description for Questions 2-3. Three different washing solutions are being compared to study their effectiveness in retarding bacteria growth in five-gallon milk containers. The analysis is done in a laboratory, and only three trials can be run on any day. Because days could represent a potential source of variability, the experimenter decides to use a model that reduces experimental error (and hence increases precision) by grouping days into blocks. Observations are taken for four days, values in table below show measurement of effectiveness (bacteria growth rate after using the solution) for each day and solution type. (refer to 2nd Image Uploaded below) Question 2. Select the correct statement below. A.) We should use a randomized block design using a two-way ANOVA model without an interaction term between Solution and Day and with a blocking factor for Days. B.) We should use a randomized block design using a two-way ANOVA model without an interaction term between Solution and Day and with a blocking factor for Solution. C.) We should use a randomized block design using a two-way ANOVA model without an interaction term between Solution and Day and with a blocking factor for Bacteria growth. D.) We should use a one-way ANOVA using Solution as the Factor. 3. Washington.csv: dataset below Solution Day Result 1 1 13 1 2 22 1 3 18 1 4 39 2 1 16 2 2 24 2 3 17 2 4 44 3 1 5 3 2 4 3 3 1 3 4 22 Use the datafile washing.csv, which represents the study data discussed in Question 5. Save the data file in your local folder that you use as your R working directory. Keep in mind that when you download the datafile by clicking on the link "washing.csv" above BB Learn may change its name such as "washing(1).csv". Once you download it make sure to change the file name manually to "washing.csv" so that the code below runs without problems. Analyze the data from this study (use a significance level α = 0.05) using the R code below and using the modeling approach you selected in Question 5. Based on the R output, which statement is correct? # read the data file and make sure the factors are recognized as factors by filling out the blank part in the code below wash <- read.csv("washing.csv", as.is =T) wash$ <- as.factor(wash$ ) wash$ <- as.factor(wash$ ) # run the model by filling out the blank part in the code below summary(aov( )) A.) At the significance level 0.05, we fail to reject the null hypothesis that Days have an impact on retarding bacteria growth in milk containers. B.) The degrees of freedom associated with testing the null hypothesis that different levels of the factor Solution have no impact on retarding bacteria growth in milk containers is 2. C.) The degrees of freedom associated with testing the null hypothesis that different levels of the factor Day have no impact on retarding bacteria growth in milk containers is 6. D.) The F statistic associated with testing the null hypothesis associated with the levels of Solution and their impact on retarding bacteria growth in milk containers is 42.71.
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Figure 2 shows the results of the Tukey test to test pairwise differences at the significance level 0.05 for the additive model using design and region with regards to their impact on the survey responses.
Figure 2.(1st Image uploaded below)
Tukey test results showing pairwise factor level comparison with regards to impact on the survey responses. P adj shows the p value for each pairwise level comparison. P values with 0.0000000 indicate that the p value is < 0.00000001.
Considering a significance level of alpha = 0.05, select the correct statement below.A.) For region, all pairwise Region levels differ from each other significantly with regards to survey responses.
B.) For design, all pairwise Design levels differ from each other significantly with regards to survey responses.
C.) The average survey response using Design 3 is 175.58 higher than the average survey response using Design 2.
D.) Designs 1 and 3 do not differ significantly; but Design 2 is significantly different than Design 1, and Design 2 is significantly different than Design 3 with regards to survey responses.
2.
Use the following description for Questions 2-3.
Three different washing solutions are being compared to study their effectiveness in retarding bacteria growth in five-gallon milk containers. The analysis is done in a laboratory, and only three trials can be run on any day. Because days could represent a potential source of variability, the experimenter decides to use a model that reduces experimental error (and hence increases precision) by grouping days into blocks. Observations are taken for four days, values in table below show measurement of effectiveness (bacteria growth rate after using the solution) for each day and solution type.
(refer to 2nd Image Uploaded below)
Question 2.
Select the correct statement below.
| A.) |
We should use a randomized block design using a two-way ANOVA model without an interaction term between Solution and Day and with a blocking factor for Days. |
|
| B.) |
We should use a randomized block design using a two-way ANOVA model without an interaction term between Solution and Day and with a blocking factor for Solution. |
|
| C.) |
We should use a randomized block design using a two-way ANOVA model without an interaction term between Solution and Day and with a blocking factor for Bacteria growth. |
|
| D.) |
We should use a one-way ANOVA using Solution as the Factor. |
3.
Washington.csv: dataset below
|
Solution |
Day | Result |
| 1 | 1 | 13 |
| 1 | 2 | 22 |
| 1 | 3 | 18 |
| 1 | 4 | 39 |
| 2 | 1 | 16 |
| 2 | 2 | 24 |
| 2 | 3 | 17 |
| 2 | 4 | 44 |
| 3 | 1 | 5 |
| 3 | 2 | 4 |
| 3 | 3 | 1 |
| 3 | 4 | 22 |
Use the datafile washing.csv, which represents the study data discussed in Question 5. Save the data file in your local folder that you use as your R working directory. Keep in mind that when you download the datafile by clicking on the link "washing.csv" above BB Learn may change its name such as "washing(1).csv". Once you download it make sure to change the file name manually to "washing.csv" so that the code below runs without problems.
Analyze the data from this study (use a significance level α = 0.05) using the R code below and using the modeling approach you selected in Question 5. Based on the R output, which statement is correct?
# read the data file and make sure the factors are recognized as factors by filling out the blank part in the code below
wash <- read.csv("washing.csv", as.is =T)
wash$ <- as.factor(wash$ )
wash$ <- as.factor(wash$ )
# run the model by filling out the blank part in the code below
summary(aov( ))
| A.) |
At the significance level 0.05, we fail to reject the null hypothesis that Days have an impact on retarding bacteria growth in milk containers. |
|
| B.) |
The degrees of freedom associated with testing the null hypothesis that different levels of the factor Solution have no impact on retarding bacteria growth in milk containers is 2. |
|
| C.) |
The degrees of freedom associated with testing the null hypothesis that different levels of the factor Day have no impact on retarding bacteria growth in milk containers is 6. |
|
| D.) |
The F statistic associated with testing the null hypothesis associated with the levels of Solution and their impact on retarding bacteria growth in milk containers is 42.71. |
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