Solution
Bezawada Arun answered on
Aug 22 2021
HW11
MGMT 650
Summer 2020 Week 11 Homework Questions
(Last updated 7/8/2020)
Chi Square
Saeko has a yarn shop and wants to test her theory on what types of colors she is selling.
She believes that Black, White, the Primary Colors, and Tertiary colors sell in equal amounts.
The primary colors are blue, red, and yellow; while the tertiary colors are Brown, Green, and Purple.
Test Saeko's theory using the 5 step hypothesis testing analysis and Chi Square at the .10 level of significance.
Here is a pivot table that shows Saeko the number of yards that were sold in the various yarn types during the busiest weekend of her shop last year.
Row Labels Count of Color Type Sum of Yards
Black 23 35856
Blue 16 17053
Brown 13 13426
Green 12 12509
Purple 12 12131
Red 8 8393
White 26 37666
Yellow 12 12874
(blank)
Grand Total 122 149908
1) Using the pivot table, fill in the blanks in the following table:
Primary Colors consists of the sum of Blue, Red, and Yellow yarn sold
Tertiary Colors consists of the sum of Brown, Green, and Purple Colors Sold.
The Total in this chart must equal the Grand Total, Cell D19 in the above table.
x p count x*p(x) (x-mean)^2*p(x)
Black 35,856.00 0.2391867012 23 8,576.28 647,891.76
White 37,666.00 0.2512607733 26 9,463.99 6,772.63
Primary Colors 38,320.00 0.255623449 36 9,795.49 171,118.47
Tertiary Colors 38,066.00 0.2539290765 37 9,666.06 80,824.98
Total 149,908.00 1 122 37501.8214371481 906607.842598324
This table represents the observed data in the Chi Square analysis.
Find the Expected values for each of the colors. Saeko expects that the colors sell in equal amounts.
Color Type Sum of Yards
Black 8,576.28
White 9,463.99
Primary Colors 9,795.49
Tertiary Colors 9,666.06
Total 37,501.82
Subtract the Expected values from the observed values
Color Type Sum of Yards
Black 27,279.72
White 28,202.01
Primary Colors 28,524.51
Tertiary Colors 28,399.94
Square the values just found
Color Type Sum of Yards
Black 744,183,212.90
White 795,353,464.71
Primary Colors 813,647,638.36
Tertiary Colors 806,556,351.96
Divide each square by the expected value and add togethe
Color Type Sum of Yards
Black 86,772.26
White 84,039.97
Primary Colors 83,063.50
Tertiary Colors 83,442.10
Total 337,317.83
2) This total is your Chi Square test statistic
Use the 5 step hypothesis testing procedure to determine if Saeko's hypothesis that the colors sell in equal amounts is true.
What is the null hypothesis? There is no significant difference between the colors that sell in equal amounts
What is the alternative hypothesis? There is a significant difference between the colors that sell in equal amounts
What is the level of significance? 0.10
3) What is the Chi Square test statistic? 337,317.83
4) What is the Chi Square critical Value? Use =CHISQ.INV()
10.1653138054
What is your answer to Saeko? State both the statstical answer (reject or do not reject, and what hypothesis), and also state your answer in English: What can Saeko learn from the data?
Since the calculated value is greater than critical value
Then we say that the alternative hypothesis is accepted.
It can be infered that the data is not fit for the model
ANOVA
Saeko owns a yarn shop and want to expands her color selection.
Before she expands her colors, she wants to find out if her customers prefer one
and
over another
and. Specifically, she is...