A mathematics department has been experimenting with four different delivery methods for content in their Algebra courses, One method is the traditional lecture (method I), the second is a hybrid format with half the class time online and the other half face-to-face (method II), the third is online (method III), and the fourth is a model from which students obtain their lectures and do their work in a lab with an instructor available for assistance (method IV). To assess the effectiveness of the four methods, students in each approach are given a final exam with the results shown in the accompanying table. Do the data suggest that any method has a different mean score from the others? Complete parts (a) through (h) below. Click here to view the data table. Click here to view the table of critical values for the correlation coefficient. X Final exam scores ANOVA Table Source DF SS MS F Method | Method II Method Ill Method IV Factor 3 1142.89 380.96 2.52 0.08 Error 26 3933.81 151.3 79 82 85 89 Total 29 5076.7 84 50 56 91 85 83 71 83 Should the null hypothesis be rejected? 65 71 68 60 Do not reject Ho: there is insufficient evidence to conclude that a method has a different mean score from the others. 92 65 64 83 69 38 78 74 (f) Shown are side-by-side boxplots of each method. Do these boxplots support the results obtained in part (e)? 83 60 61 64 O A. No, because the boxplots show that all of the means are significantly different. 65 B. Yes, because the boxplots do not show that at least one of the means is significantly different. 89 O C. No, because the boxplots show that the means are not significantly different. D. Yes, because the boxplots show that at least one of the means is significantly different. Print Done (g) Interpret the P-value. Select the correct choice below and fill in the answer box within your choice. (Round to three decimal places as needed.) O A. Assuming the null hypothesis is false, the probability this much or more variability occurs in the four sample means is when the experiment is repeated many times. O B. Assuming the null hypothesis is false, the probability this much or more variability occurs in the four sample means is in every experiment O C. Assuming the null hypothesis is true, the probability this much or more variability occurs in the four sample means is when the experiment is repeated many times. O D. Assuming the null hypothesis is true, the probability this much or more variability occurs in the four sample means is in every experiment
