Question

the data for the perceived level of stress of 30 employees and each employee’s number of absences in a 120-day period are shown.

Stress Level
Low	Moderate	High
2.6	2.7	2.2
2.4	2.7	2.3
2.3	2.1	2.0
2.3	2.7	2.5
2.7	2.9	2.8
2.9	2.2	2.1
2.7	2.6	1.8
3.0	2.4	1.9
3.0	2.5	2.5
2.2	2.4	2.6

a) Write the null and alternate hypotheses for the test you suggest conducting to test for significance of difference between the three levels of stress.

b) Conduct the appropriate statistical test on the data in the file. Interpret your findings.

c) Discuss the two kinds of variance here, and indicate how they are compared to conclude a significant difference.

Answer 1

(a) We perform one way analysis of variance to compare the mean stress among the three groups at 5% level of significance.

The hypothesis of the test are

H0: The mean stress level are same among the all three groups

Ha: The mean stress level are differ among the all three groups.

(b) We found the test Statistc F = 3.602 and the P value of the test is 0.041, which is less than the level of significance alpha 0.05, therefore we reject the null hypothesis and concluded that the mean stress level are differ among the all three groups.

(c) In ANOVA table, there are two type of mean sum of square (MS) within and between the groups. These two type of error are called the variance between and within the group and the ratio of these two error are the F-Statistc or F-value. If the ratio of between and within group is one then both value of the variance would be same. If the value of test Statistc F is differ from one then there would be some change in the ratio of variance between and within group. If the difference are higher than the F critical value then we reject the null hypothesis otherwise fail to reject.