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.
Black
White
Primary Colors
Tertiary Colors
Total
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
White
Primary Colors
Tertiary Colors
Total
Subtract the Expected values from the observed values
Color Type Sum of Yards
Black
White
Primary Colors
Tertiary Colors
Square the values just found
Color Type Sum of Yards
Black
White
Primary Colors
Tertiary Colors
Divide each square by the expected value and add together
Color Type Sum of Yards
Black
White
Primary Colors
Tertiary Colors
Total
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?
What is the alternative hypothesis?
What is the level of significance?
3) What is the Chi Square test statistic?
4) What is the Chi Square critical Value? Use =CHISQ.INV()
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?
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 brand
over another brand. Specifically, she is interested in three different types of bison yarn.
As an experiment, she randomly selected 21 different days and recorded the sales of each brand.
At the .10 significance level, can she conclude that there is a difference in preference between the brands?
Misa’s Bison Yak-et-ty-Yaks Buffalo Yarns
799 776 799
784 640 931
807 822 794
675 856 920
795 616 731
875 893 837
Total 4,735.00 4,603.00 5,012.00
5) What is the null hypothesis?
What is the alternative hypothesis?
What is the level of significance?
6) Use Tools – Data Analysis – ANOVA:Single Factor
to find the F statistic:
7) From the ANOVA output: What is the F value?
8) What is the F critical value?
9) What is your decision?
Explain in statistical terms
Regression
Studies have shown that the frequency with which shoppers browse Internet retailers is related to the frequency with which they actually purchase products and/or services online. The following data show respondents age and answer to the question “How many minutes do you browse online retailers per year?”
Age (X) Time (Y)
34 123,556.00
17 92,425.00
42 250,908.00
35 204,540.00
19 77,897.00
43 197,012.00
51 195,126.00
50 177,100.00
22 83,230.00
58 140,012.00
48 265,296.00
35 189,420.00
39 235,872.00
39 230,724.00
59 238,655.00
40 138,560.00
60 259,680.00
22 93,208.00
33 91,212.00
36 153,216.00
28 77,308.00
22 56,496.00
28 106,652.00
44 242,748.00
54 195,858.00
30 178,560.00
28 190,876.00
16 98,528.00
52 169,572.00
22 79,420.00
28 167,928.00
35 215,705.00
50 146,350.00
10) Use Data > Data Analysis > Correlation to compute the correlation checking the Labels checkbox.
11) Use the Excel function =CORREL to compute the correlation. If answers for #1 and 2 do not agree, there is an error.
The strength of the correlation motivates further examination.
12) a) Insert Scatter (X, Y) plot linked to the data on this sheet with Age on the horizontal (X) axis.
b) Add to your chart: the chart name, vertical axis label, and horizontal axis label.
c) Complete the chart by adding Trendline and checking boxes
Read directly from the chart:
13) a) Intercept =
b) Slope =
c) R2 =
Perform Data > Data Analysis > Regression.
14) Highlight the Y-intercept with yellow. Highlight the X variable in blue. Highlight the R Square in orange
15) Use Excel to predict the number of minutes spent by a 22-year old shopper. Enter = followed by the regression formula.
Enter the intercept and slope into the formula by clicking on the cells in the regression output with the results.
16) Is it appropriate to use this data to predict the amount of time that a 9-year-old will be on the Internet?
If yes, what is the amount of time, if no, why?
Cleaning Data with Outlier
17) On this worksheet, make an XY scatter plot linked to the following data:
X Y
1.01 2.8482
1.48 4.2772
1.8 4.788
1.81 5.3757
1.07 2.5252
1.53 3.0906
1.46 4.3362
1.38 3.2016
1.77 4.3542
1.88 4.8692
1.32 3.8676
1.75 3.9375
1.94 5.7424
1.19 2.4752
1.31 26.2
1.56 4.5708
1.16 2.842
1.22 2.44
1.72 5.1256
1.45 4.3355
1.43 4.2471
1.19 3.5343
2 5.46
1.6 3.84
1.58 3.8552
18) Add trendline, regression equation and r squared to the plot.
Add this title. (“Scatterplot of X and Y Data”)
19) The scatterplot reveals a point outside the point pattern. Copy the data to a new location in the worksheet. You now have 2 sets of data.
Data that are more tha 1.5 IQR below Q1 or more than 1.5 IQR above Q3 are considered outliers and must be investigated.
It was determined that the outlying point resulted from data entry error. Remove the outlier in the copy of the data.
Make a new scatterplot linked to the cleaned data without the outlier, and add title (“Scatterplot without Outlier,”) trendline, and regression equation label.
X Y
1.01 2.8482
1.48 4.2772
1.8 4.788
1.81 5.3757
1.07 2.5252
1.53 3.0906
1.46 4.3362
1.38 3.2016
1.77 4.3542
1.88 4.8692
1.32 3.8676
1.75 3.9375
1.94 5.7424
1.19 2.4752
1.56 4.5708
1.16 2.842
1.22 2.44
1.72 5.1256
1.45 4.3355
1.43 4.2471
1.19 3.5343
2 5.46
1.6 3.84
1.58 3.8552
Compare the regression equations of the two plots. How did removal of the outlier affect the slope and R2? Explain why the slope and R Square change the way they did
20)