Answer to Question #182744 in Statistics and Probability for Carol

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 I Fair I Poor 94 75 I 70 I 68 90 68 I 73 I 70 85 77 I 76 I 72 80 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.

Please do not use excel.

Answer 1

$H_o:\mu=\mu_o$ , There is no differene in mean

$H_a:\mu\neq \mu_o$ There is differene in mean

  

Test Statistic :-

$f = \dfrac{\text{ MS treatment }}{\text{ MS error }} =\dfrac{296.895}{33.023}= 8.99$

Test Criteria :-

Reject null hypothesis if $f > f(α , a-1 , N-a )$

Critical value$f(0.01, 3 , 18 ) = 5.0919$ (From F table)

Since Calculated value of f i.e. 8.99 > 5.0919, we reject $H_o$

We have sufficient evidence to support the claim that there is significant difference.