Deck 14: Analysis of Variance Anova

Question 1

Consider the following data:

A) Obtain the arrays that show a decomposition for the observations. That is, complete the following arrays.

B) Find the sum of squares for each array. That is, find Treatment S.S, Residual S.S, Mean S.S, Total S.S, Total S.S (Corrected), respectively.
C) Determine the degrees of freedom for each sum of squares. That is, determine Error d.f.
and Treatment d.f., respectively.
D) Summarize by completing the ANOVA table.

Answer 1

Part A:
Part B:
Treatment S.S = 12
Residual S.S = 8
Mean S.S = 288
Total S.S = 308
Total S.S (corrected) = 20
Part C:
Error d.f. = 4
Treatment d.f. = 3
Part D:

Question 2

Use the relations for sums of squares and d.f. to complete the following ANOVA table.

Answer 2

Question 3

Perfect scores are not always attained in a test. Suppose the records from four different courses yield the following data on the number of perfect scores per test.

A) Provide a decomposition of the observations by completing the table.

B) Obtain the ANOVA table.

Answer 3

Question 4

The following table is associated with the average number of patients served,
0ver 6 days, at different months of the year.
Present the ANOVA table for these data.

Question 5

Using the table of percentage points for the F distribution, find the upper 10% point when v₁ = 8 and v₂ = 120.

A) 1.72
B) 2.34
C) 2.02

Question 6

Consider the following ANOVA table.
Carry out the F test for equality of means taking α = 0.010. Answer "The null hypothesis is rejected at level α = 0.010"
or "The null hypothesis is not rejected at level α = 0.010".

Question 7

Consider the following ANOVA table.
Test for equality of means using α = 0.100. Answer "H₀ is rejected at α = 0.100"
or "H₀ is not rejected at α = 0.100".

Question 8

There are four lecture sessions for a Statistics course but all students take common exams. The following table is associated with the average class score in six 40 point
quizzes administered during the semester.
Test for equality of means. Take α = 0.001. Answer "H₀ is rejected at α = 0.001"
or "H₀ is not rejected at α = 0.001".

Question 9

Taking $\alpha$ = 0.05 and n - k = 18, determine the appropriate percentile of the t distribution when calculating the multiple-t confidence intervals with m = 3.

Question 10

Four drug stores have a pharmacy which is open twenty-four hours a day. The following table is associated with the daily average number of patients served, outside of the normal hours 9 a.m. to 9 p.m. Data are collected each day of the week for one week.
The ANOVA table for these data is shown below.
Calculate a simultaneous 94% confidence interval for the difference in means .

Question 11

Consider the following data:

A) Provide a decomposition for the observation from these randomized block experiment. That is, complete the following tables.
B) Find the sum of squares for each array. That is, find Treatment S.S, Block S.S, Residual S.S, Mean S.S, Total S.S, and Total S.S (corrected), respectively.
C) Determine the degrees of freedom by checking the constraints for each array. That is, find Treatment d.f., Block d.f., and Residual d.f, respectively.

Question 12

Consider the following data:
Fill in the corresponding ANOVA table.

Question 13

Consider the following data:
Perform an analysis of variance for these data. Use α = 0.05. Answer "The treatment effects are (are not) significant"
and "The block effects are (are not) significant".

Question 14

Consider the following ANOVA table with treatment means = 70.20, = 65.40, and = 79.60.
Obtain simultaneous confidence intervals for the pairwise differences in mean for the three treatments. Take α = 0.05.

Question 15

Consider the following data:
Find the residuals array.

Question 16

16 Three processes for creating flame-retardant fabric are under con- sideration. Three dresses are made from Fabric A, two from Fabric B, and three from Fabric C. The response of interest is the verti- cal damage(inches) to the dress when a paper tab, attached to the bottom, is ignited.

(a) Obtain the arrays that show a decomposition for the observa- tions.
(b) Create the ANOVA table.
(c) Conduct a test for equality of the three means. Take α = .05.