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?

Method 1 Method 2 Method 3 Method 4

81 89 83 87

77 55 61 95

88 83 69 85

64 79 73 60

85 61 66 84

71 40 78 70

70 60

63 59

60

91

Use any method but follow the PHANTOMS acronym

P - Parameter Statement

H - Hypotheses

A - Assumptions & Conditions

N - Name the Test

T - Test Statistic

O - Obtain the P-Value or Critical Value

M - Make a Decision about the Null Hypothesis

S - State Your Conclusion About the Claim