blem: rologis studying the elect culture media and 2 preselected different times on the growth of a particular virus. She performs a balanced design with 6 plates for each of the treatment combinations. The 24 measurements were taken in a completely randomized order. Medium Time 12 1 2 륨 18 12 18 9 8 2 27.5 38.0 27.2 29.3 24 29.7 37.6 27.1 30.6 Describe the relationship of the factors using the plot below. 15.4 40.0 26.8 31.6 Data 21.0 37.3 28.6 32.8 20.8 40.9 31.1 32.5 12 hrs 18 hrs 19.1 38.8 25.4 33.6 Test for factor A: (if necessary) Ho: (in symbols and words) Ha: (in symbols and words) Test statistic formula: Value of the test statistic: p-value: Decision: Conclusion: Test for factor B: (if necessary) Ho: (in symbols and words) Ha: (in symbols and words) Test statistic formula: Value of the test statistic: p-value: Decision: Conclusion: * Explain briefly how you should proceed given the result of recent hypothesis tests. If all assumptions of parametric test were satisfied, * Based on R outputs on the sheet provided, summarize your insights about the effects of 2 different culture media and 2 different times on the growth of a particular virus.

College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Counting And Probability
Section9.3: Binomial Probability
Problem 1E: A binomial experiment is UDC in which there are exactly __________ outcome. One outcome is called...
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Answer the last two portion with the red asterisk (*)

POULTRY PROBLEM
Problem: A virologist is interested in studying the effects of 2 preselected different
culture media and 2 preselected different times on the growth of a particular virus.
She performs a balanced design with 6 plates for each of the treatment
combinations. The 24 measurements were taken in a completely randomized
order.
Test for factor A: (if necessary)
Ho: (in symbols and words)
Ha: (in symbols and words)
Test statistic formula:
Value of the test statistic:
推維維推
p-value:
Decision:
Conclusion:
Medium
Time
Data
12
27.5
38.0
27.2
29.7
37.6
15.4
40.0
26.8
21.0
37.3
28.6
20.8
40.9
31.1
19.1
1
18
38.8
12
27.1
25.4
2
Test for factor B: (if necessary)
Ho: (in symbols and words)
Ha: (in symbols and words)
Test statistic formula:
18
29.3
30.6
31.6
32.8
32.5
33.6
Describe the relationship of the factors using the plot below.
Value of the test statistic:
p-value:
Decision:
Co
usion:
* Explain briefly how you should proceed given the result of recent hypothesis tests.
If all assumptions of parametric test were satisfied,
20
10
12 hrs
18 hrs
* Based on R outputs on the sheet provided, summarize your insights about
the effects of 2 different culture media and 2 different times on the growth
of a particular virus.
1.0
2.0
Medium
* Determine whether they exhibit strong, intermediate or no interaction. Provide explanation.
Test the assumption of the parametric test at 5% level of significance.
Test
p-value
Conclusion
R outputs
Homogeneity of Variances
Shapiro-Wilk Normality Test
*TC1:
p-value
Conclusion
data: Medium 1 & Time 12
data:
Medium 1
& Time 18
Shapiro-Wilk normality test
W = 0.93239,
p-value = 0.5987
data:
Shapiro-Wilk normality test
W = 0.91981,
*TC2:
*TC3:
*TC4:
p-value = 0.504
Medium 2 & Time 12
data:
Medium 2 & Time 18
*TC – Treatment Combination
Shapiro-Wilk normality test
W = 0.86098
p-value = 0.2318
Shapiro-Wilk normality test
W= 0.96619
p-value = 0.8503
What is the most appropriate analysis given the results on testing of assumptions?
Justify your answer.
Levene's Test for Homogeneity of Variance (center = "mean")
Df F value Pr (>F)
group
5.474 0.006521
summary(aov(wk8_data$Data~wk8_data$Medium*wk8_data$Time))
Df Sum Sq Mean Sq F value
Pr(>F)
0.531
wk8_data$Medium
wk8_data$Time
1
3.8
3.8
0.406
1 633.5
633.5 68.385 6.96e-08 ***
wk8_data$Medium:wk8_data$Time
1
233.8
233.8 25.235 6.51e-05 ***
Residuals
20 185.3
9.3
Suppose all assumption of parametric test were satisfied, perform necessary
parametric tests of hypothesis at 5% level of significance.
Signif. codes: 0 ****' 0.001 **' 0.01 **' 0.05 '.' 0.1 ' ' 1
Test for Interaction of factor A and B
Analysis of Variance
Ho: (in symbols and words)
Ha: (in symbols and words)
Test statistic formula:
Value of the test statistic:
Df Sum Sq Mean Sg F value
871.0
Pr (>F)
31.34 9.35e-08 ***
Treatment Combination
Residuals
3
290.32
20
185.3
9.26
p-value:
Decision:
Conclusion:
Signif. codes:
0 ****! 0.001 '**' 0.01 '*
0.05 '.' 0.1 ' 1
Kruskal-Wallis Rank Sum Test
data:
wk8 data$Data by Treatment Combinations
Kruskal-Wallis chi-squared = 19.007, df = 3, p-value = 0.0002725
Data
Transcribed Image Text:POULTRY PROBLEM Problem: A virologist is interested in studying the effects of 2 preselected different culture media and 2 preselected different times on the growth of a particular virus. She performs a balanced design with 6 plates for each of the treatment combinations. The 24 measurements were taken in a completely randomized order. Test for factor A: (if necessary) Ho: (in symbols and words) Ha: (in symbols and words) Test statistic formula: Value of the test statistic: 推維維推 p-value: Decision: Conclusion: Medium Time Data 12 27.5 38.0 27.2 29.7 37.6 15.4 40.0 26.8 21.0 37.3 28.6 20.8 40.9 31.1 19.1 1 18 38.8 12 27.1 25.4 2 Test for factor B: (if necessary) Ho: (in symbols and words) Ha: (in symbols and words) Test statistic formula: 18 29.3 30.6 31.6 32.8 32.5 33.6 Describe the relationship of the factors using the plot below. Value of the test statistic: p-value: Decision: Co usion: * Explain briefly how you should proceed given the result of recent hypothesis tests. If all assumptions of parametric test were satisfied, 20 10 12 hrs 18 hrs * Based on R outputs on the sheet provided, summarize your insights about the effects of 2 different culture media and 2 different times on the growth of a particular virus. 1.0 2.0 Medium * Determine whether they exhibit strong, intermediate or no interaction. Provide explanation. Test the assumption of the parametric test at 5% level of significance. Test p-value Conclusion R outputs Homogeneity of Variances Shapiro-Wilk Normality Test *TC1: p-value Conclusion data: Medium 1 & Time 12 data: Medium 1 & Time 18 Shapiro-Wilk normality test W = 0.93239, p-value = 0.5987 data: Shapiro-Wilk normality test W = 0.91981, *TC2: *TC3: *TC4: p-value = 0.504 Medium 2 & Time 12 data: Medium 2 & Time 18 *TC – Treatment Combination Shapiro-Wilk normality test W = 0.86098 p-value = 0.2318 Shapiro-Wilk normality test W= 0.96619 p-value = 0.8503 What is the most appropriate analysis given the results on testing of assumptions? Justify your answer. Levene's Test for Homogeneity of Variance (center = "mean") Df F value Pr (>F) group 5.474 0.006521 summary(aov(wk8_data$Data~wk8_data$Medium*wk8_data$Time)) Df Sum Sq Mean Sq F value Pr(>F) 0.531 wk8_data$Medium wk8_data$Time 1 3.8 3.8 0.406 1 633.5 633.5 68.385 6.96e-08 *** wk8_data$Medium:wk8_data$Time 1 233.8 233.8 25.235 6.51e-05 *** Residuals 20 185.3 9.3 Suppose all assumption of parametric test were satisfied, perform necessary parametric tests of hypothesis at 5% level of significance. Signif. codes: 0 ****' 0.001 **' 0.01 **' 0.05 '.' 0.1 ' ' 1 Test for Interaction of factor A and B Analysis of Variance Ho: (in symbols and words) Ha: (in symbols and words) Test statistic formula: Value of the test statistic: Df Sum Sq Mean Sg F value 871.0 Pr (>F) 31.34 9.35e-08 *** Treatment Combination Residuals 3 290.32 20 185.3 9.26 p-value: Decision: Conclusion: Signif. codes: 0 ****! 0.001 '**' 0.01 '* 0.05 '.' 0.1 ' 1 Kruskal-Wallis Rank Sum Test data: wk8 data$Data by Treatment Combinations Kruskal-Wallis chi-squared = 19.007, df = 3, p-value = 0.0002725 Data
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