Are the means for the final exams the same for all statistic

Are the means for the final exams the same for all statistics class delivery types? The table below shows the scores on final exams from several randomly selected classes that used the different delivery types. Assume that all distributions are normal, the four population standard deviations are approximately the same, and the data were collected independently and randomly. Use a level of significance of 0.05.

Online

Hybrid

Face-to-face

72

83

80

84

73

78

77

84

84

80

81

81

81

86

79

82

Solution

Ho: all mean are equal (i.e. null hypothesis)

Ha: at least one mean is different (i.e. alternative hypothesis)

The test statistic is

F=0.64

The p-value of F test is 0.5437

Since the p-value is larger than 0.05, we do not reject Ho.

So we can conclude that the means for the final exams are the same for all statistics class delivery types