Answer to Question #171763 in Statistics and Probability for Moon Shah

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.

(20 marks)

Answer 1

To test the difference the null and alternative hypotheses are defined as follows:

H₀: μ₁ = μ₂ = μ₃ = μ₄

H₁: At least two means are differ

This can be analysed using a 1-way ANOVA.

The F value calculated 8.99 > critical value F(crit) of 5.09. The probability to obtain this result by chance (P-value) was calculated as 0.00074 or 0.074 %. So, we are able to conclude that there was significant difference in average between the four rating categories.