ANOVA Mean Hypothesis Test
Directions: Use the printouts to answer the following questions.
a) Give the null and alternative hypothesis.
b) Check the assumptions for a One-Way ANOVA test.
c) Write a sentence to explain the F test statistic.
d) Use the F test statistic and Critical Value to determine if the sample data significantly disagrees with
the null hypothesis. Explain your answer.
e) Use the P-value and Significance Level to answer the following:
-Write the P-value sentence.
-Could the sample data or more extreme have occurred because of sampling variability or is it unlikely
that the sample data occurred because of sampling variability? Explain your answer.
f) Should we reject the null hypothesis or fail to reject the null hypothesis? Explain your answer.
g) Write a conclusion for the hypothesis test addressing evidence and the claim.
h) What is the variance between the groups? What is the variance within the groups? Was the variance
between significantly higher than the variance within? Explain how you know.
i) Was the categorical and quantitative variables related or not. Explain your answer.
The Scenario: A census of Math 075 pre-stat students was taken in the fall 2015 semester. The students were
separated into three sleep groups: low amount of sleep, moderate amount of sleep, high amount of
sleep. They were also asked how many total units they have completed at the college. Though the data
was not random, you can assume it was representative of Math 075 students at COC. Use a 10%
significance level and the following statistics, graphs and ANOVA printout to test the claim that sleep is
not related to the total number of units completed
ANOVA Information:
Source of Variation
Degrees of
Freedom
Sum of Squared
Mean Sum of Squares
F Test Statistic
F Critical Value
p-Value
Treatment (Between Groups)
2 2822.35625 1411.17813 1.83387 2.3133 0.16087
Error (Within Groups)
497 382446.38503 769.50983
Total 499 385268.74128
Descriptive Statistics:
Variable Mean Standard Deviation N total
Low Sleep Group 32.952 28.586 42
Medium Sleep Group
32.990 27.585 398
High Sleep Group 25.675 28.178 60