Answer to Question #182840 in Statistics and Probability for royston

Question

Professor Albert Francis had students in his Psychology 201 class rate his performance. The ratings are kept from the professor till release of the course marks. The course marks are shown in the table below, under the respective rating given by the students.

Performance Rating

Excellent Good Fair Poor

94 75 70 68

90 68 73 70

85 77 76 72

80 83 78 65

88 80 74

68 65

65

Table Q5

Apply and perform an appropriate test to check if there is a difference in the mean marks received by students in each of the rating categories. Show all relevant workings and steps in the test, and test at 1% level of significance.

Answer 1

By using Excel

Select Anova: Single Factor, then enter the data ranges, selected Grouped By: Rows and set Alpha to 0.01 (1%). Select a suitable output option and then OK. This returned a table of data as shown below.

The F value calculated was 8.9906. This comfortably exceeds the stated critical value (F_crit) of 5.0918, and the probability of obtaining this result by chance (P-value) was calculated as 0.00074 (0.074%); hence the professor was able to reject the null hypothesis and conclude that there was a significant difference in in the mean marks received by students in each of the rating categories, since P <0.01.