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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1/ need help with c,d,e
The data in the accompanying table represent the number of com plants in randomly sampled rows (a 17-foot by 5-inch strip) for various types of plots. An agricultural researcher wants to know whether the mean numbers of plants for each plot type are equal. Complete parts (a) through (e) below. Click here to view the data table. Click here to view the table of critical values for the correlation coefficient. Table of critical values for the correlation coefficient. (a) Write the null and alternative hypotheses. Choose the correct answer below. Sample Size, n Critical Value O 0.880 0.888 0.898 O A. Ha: at least one of the means is different and H,: Haludoe =Hspring "Pno till 6 O B. Ho: Hsludge "Hspring "Hno till and H: at least one of the means is different 8 0.906 0.912 0.918 O C. Ho: Hsludge " Hspring and H: the means are different 9. Corn plants 10 11 O D. Ho: Hsludge "Hspring " Hno till and H: Hsludge Hspring Hno til 0.923 12 0.928 (b) Which of the following requirements must be satisfied to use the one-way ANOVA procedure? Select all that apply. 13 14 15 16 0.932 0.935 0.939 0.941 0.944 0.946 Sludge Plot Spring Disk No Till O A. The populations must be normally distributed. O B. There must be k simple random samples, each from the same population, or k randomized experiments with a single treatment. 25 34 32 27 29 27 17 18 19 20 O C. The k samples must be independent of each other. 34 31 28 29 35 30 O D. There must be k simple random samples, one from each of k populations, or a randomized experiment with k treatments. 0.949 0.951 0.952 0.964 28 33 25 O E. The populations must have the same variance. 28 32 30 21 OF. The populations must have the same mean. 22 23 0.956 (c) Use the following one-way ANOVA table to test the hypothesis of equal means at the a= 0.05 level of significance. 0.957 24 25 0.959 One-way ANOVA: Sludge Plot, Spring Disk, No Till Print Done Source 30 0.960 DF 2 15 MS Factor 56.33 100.17 28.17 4.22 0.035 Error 6.68 Total 17 156.5 Should the null hypothesis be rejected? Print Done
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Transcribed Image Text:The data in the accompanying table represent the number of com plants in randomly sampled rows (a 17-foot by 5-inch strip) for various types of plots. An agricultural researcher wants to know whether the mean numbers of plants for each plot type are equal. Complete parts (a) through (e) below. Click here to view the data table. Click here to view the table of critical values for the correlation coefficient. Table of critical values for the correlation coefficient. (a) Write the null and alternative hypotheses. Choose the correct answer below. Sample Size, n Critical Value O 0.880 0.888 0.898 O A. Ha: at least one of the means is different and H,: Haludoe =Hspring "Pno till 6 O B. Ho: Hsludge "Hspring "Hno till and H: at least one of the means is different 8 0.906 0.912 0.918 O C. Ho: Hsludge " Hspring and H: the means are different 9. Corn plants 10 11 O D. Ho: Hsludge "Hspring " Hno till and H: Hsludge Hspring Hno til 0.923 12 0.928 (b) Which of the following requirements must be satisfied to use the one-way ANOVA procedure? Select all that apply. 13 14 15 16 0.932 0.935 0.939 0.941 0.944 0.946 Sludge Plot Spring Disk No Till O A. The populations must be normally distributed. O B. There must be k simple random samples, each from the same population, or k randomized experiments with a single treatment. 25 34 32 27 29 27 17 18 19 20 O C. The k samples must be independent of each other. 34 31 28 29 35 30 O D. There must be k simple random samples, one from each of k populations, or a randomized experiment with k treatments. 0.949 0.951 0.952 0.964 28 33 25 O E. The populations must have the same variance. 28 32 30 21 OF. The populations must have the same mean. 22 23 0.956 (c) Use the following one-way ANOVA table to test the hypothesis of equal means at the a= 0.05 level of significance. 0.957 24 25 0.959 One-way ANOVA: Sludge Plot, Spring Disk, No Till Print Done Source 30 0.960 DF 2 15 MS Factor 56.33 100.17 28.17 4.22 0.035 Error 6.68 Total 17 156.5 Should the null hypothesis be rejected? Print Done
(c) Use the following one-way ANOVA table to test the hypothesis of equal means at the a=0.05 level of significance. One-way ANOVA: Sludge Plot, Spring Disk, No Till Source DF 2 MS 28.17 F 4.22 P Factor 56.33 0.035 Error 15 100.17 6.68 Total 17 156.5 Should the null hypothesis be rejected? Họ: there is V evidence to conclude that the mean numbers of plants for each plot type are not equal. (d) Shown are side-by-side boxplots of each type of plot. Do these boxplots support the results obtained in part (c)? Choose the corect answer below. O A. Yes, because the boxplots show that the means are not significantly different. O B. Yes, because the boxplots show that at least one of the means is significantly different. OC. No, because the boxplots do not show that at least one of the means is significantly different. No TiH Spring Disk OD. No, because the boxplots show that all of the means are significantly different. Sludge Plot- 25 30 Number of Plants 35 (e) Verify that the residuals are normally distributed. Probability Plot of Residuals The normal probability plot and linear correlation coefficient, r, is shown on the right. How does the normal probability plot of the residuals show that the residuals are normally distributed? O A. The plot is linear enough, because r is less than the critical value. OB. The plot is not linear enough, because r is greater than the critical value. -4.17 OC. The plot is linear enough, because r is greater than the critical value. Residuals OD. The plot is not linear enough, because r is less than the critical value. r=0.984 O E. There is at least one outlier.
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Transcribed Image Text:(c) Use the following one-way ANOVA table to test the hypothesis of equal means at the a=0.05 level of significance. One-way ANOVA: Sludge Plot, Spring Disk, No Till Source DF 2 MS 28.17 F 4.22 P Factor 56.33 0.035 Error 15 100.17 6.68 Total 17 156.5 Should the null hypothesis be rejected? Họ: there is V evidence to conclude that the mean numbers of plants for each plot type are not equal. (d) Shown are side-by-side boxplots of each type of plot. Do these boxplots support the results obtained in part (c)? Choose the corect answer below. O A. Yes, because the boxplots show that the means are not significantly different. O B. Yes, because the boxplots show that at least one of the means is significantly different. OC. No, because the boxplots do not show that at least one of the means is significantly different. No TiH Spring Disk OD. No, because the boxplots show that all of the means are significantly different. Sludge Plot- 25 30 Number of Plants 35 (e) Verify that the residuals are normally distributed. Probability Plot of Residuals The normal probability plot and linear correlation coefficient, r, is shown on the right. How does the normal probability plot of the residuals show that the residuals are normally distributed? O A. The plot is linear enough, because r is less than the critical value. OB. The plot is not linear enough, because r is greater than the critical value. -4.17 OC. The plot is linear enough, because r is greater than the critical value. Residuals OD. The plot is not linear enough, because r is less than the critical value. r=0.984 O E. There is at least one outlier.
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