Question

College students were asked to rate the spring festivals at university in years 2016, 2017, and 2018. The following table shows the students’ ratings on a scale from 0 to 100 where larger values are assigned to better activities. Construct an ANOVA table and determine whether there is a significant difference among the student appreciation of spring festivals for different years. Assume a significance level of α = 0.05.

2016	2017	2018
72	93	87
58	70	70
71	76	90
56	69	85
45	86	76
73	65	94
68	70	85

Answer 1

Hypothesis:

H0: The mean rating for the three years is the same.

H1: The mean rating for the three years is not the same.

Let ratings of 2016 be represented by Group A =((72, 58, 71, 56, 45, 73, 68))

Let ratings of 2017 be represented by Group B = (93, 70, 76, 69, 86, 65, 70)

Let ratings of 2018 be represented by Group C= (87, 70, 90, 85, 76, 94, 85)

(g represents grand total)

We find the mean of both groups and the the entire data

No of observation in each group

no. of groups = k = 3

Next we find the difference between each observation in the group with mean of the group and square it up.

example In group A we take the first observation and minus it the group mean (72-63.28)^2,this is done for each observation and for every group and summed up

Sum of square within the groups

Mean sum of square within the groups

Sum of square between the groups

Mean sum of square between the groups

Using the F table we find pvalue with df1 = 2 and df2=18

pvalue = 0.00340

Since the pvalue is less than 0.05, we reject the null hypothesis and conclude that the mean rating for the three years is not the same.