Statistics 106: Winter 2020 – Homework 4

Order ready-to-submit essays. No Plagiarism Guarantee!

Note: Our papers are 100% human-written, not AI-generated. 

We Write Essays for Students

Tell us about your assignment and we will find the best writer for your paper

Get Help Now!

STATISTICS 106

Winter 2020

Homework 4

A study aims to test the effect of price discounts and package size on the sales of saltine crackers. Three levels of discount (10%, 20% and 30%) and three package sizes (Small/Medium/Large) are tested. Five stores are randomly assigned to each combination of discount and package

size. The sample means of
sales in thousand dollars observed over an entire month for each discount-size
combination are reported in Table 1.

				Package size (Factor B)
				Small		Medium		Large
							Y i··
	10%	8		11		18
Discount	20%	11		13		20
(Factor A)	30%	17		18		24
		Y ·j·							Y··· =

Table 1: Sample means of
saltine cracker sales in thousand dollars across the levels of discount and
package size.

1. Identify factors, their
   type and nature, treatments, experimental units and the response variable. (4p)

• Identify the individual
  sample size n, the number of levels of discount and package size, a and b, the
  number of treatments r, the overall sample size n_T . (4p)

• Which kind of experimental design is this? Why?
  (4p)

• Produce the interaction
  plot of Factor A (discount) and Factor B (package size), and viceversa,
  commenting about the main effects of both factors and their interactions. (8p)

• Complete Table 1. Then,
  calculate the sum of treatment squares for factor A (SSA), factor B (SSB) and
  their interactions (SSAB). Finally, complete Table 2. (8p)

• Test for the overall
  presence of main effects for factors A and B and of their interactions. (6p)

• Can the simulatenous effect µ₁₁ be assumed equal to 12?
  Perform the individual-wise test at a significance level of 5% and comment.
  (4p)

• Derive a confidence
  interval at 95% for µ_1·,
  both individual-wise and family-wise over the family composed by all the
  row-wise means µ_1i,
  i = 1, . . . , a. (8p)

1

Source of	Sum of	Degrees of	M S
Variation	Squares (SS)	Freedom (df)	=	SS
df
Factor	SSA =		MSA =
A
Factor	SSB =		MSB =
B
Interaction	SSAB =		MSAB =
AB
Between	SSTR =		MSTR =
treatments
Within	SSE = 1000		MSE =
treatments
Total	SSTO =

Table 2: Saltine crackers sales by discount and package size: two-factor
analysis of variance

• Test the null hypothesis µ₂₃ − µ₂₂ = 0 at a significance
  level of 5%, both individual-wise and family-wise (over all pairwise differences
  involving the simultaenous effects). Comment. (8p)

1. Derive the confidence
   interval at 95% for the contrast −¹₄ µ₃₁ + ¹₂ µ₃₂ − ¹₄ µ₃₃, both individual-wise and family-wise (over the
   infinite-dimensional family of contrasts in-volving all simultaneous effects).
   Comment. (8p)

Suppose now that Table 1 is
referred to only one store for each discount-size combina-tion instead of five.

1. Which is the effect of this
   change on the underlying model we allow for the data? Explain. (8p)

1. Produce a new ANOVA table with the respective
   degrees of freedom. (6p)

1. Test for the overall
   presence of main effects for factors A and B. Are these tests reliable? (6p)

1. Estimate an individual-wise confidence interval
   at 95% for µ_2·. (4p)

1. Estimate the treatment mean
   for stores with a 20% discount and a medium package size. Comment. (6p)

1. Perform Tukey’s additivity
   test with a significance level of 5% and 1%. Comment. (8p)

If
you need answers to this assignment, WhatsApp/Call +1 646 978 1313 or send us
an email to admin@shrewdwriters.com
and we will reply instantly.

The post Statistics 106: Winter 2020 – Homework 4 appeared first on Shrewd Writers.

Welcome to originalessaywriters.com, our friendly and experienced essay writers are available 24/7 to complete all your assignments. We offer high-quality academic essays written from scratch to guarantee top grades to all students. All our papers are 100% plagiarism-free and come with a plagiarism report, upon request

Tell Us “Write My Essay for Me” and Relax! You will get an original essay well before your submission deadline.