statistics question
Below is an excel document for the homework
HW11
MGMT 650
Summer 2020 Week 11 Homework Questions
(Last updated 4/1/2020)
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.
(Optional) Use the “Pivot Table Data” tab to create 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.
Here is the pivot table that you should have created. It is optional so that you can practice your pivot table skills.
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 that you just created, 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?
Pivot Table Data
Customer Color Name Color Type Yards Meters
1 Coriander White 1155 1,056.13
2 Black Black 1504 1,375.26
3 Daffodil Yellow 904 826.62
4 Black Black 1850 1,691.64
5 Opal Blue 1497 1,368.86
6 Toffee Brown 929 849.48
7 Ruby Red 918 839.42
8 Ash Blue 584 534.01
9 Black Black 2363 2,160.73
10 Ash Blue 816 746.15
11 Black Black 1685 1,540.76
12 Whirlpool Blue 1402 1,281.99
13 Verde Green 972 888.80
14 Regal Purple 590 539.50
15 Lynx Brown 1263 1,154.89
16 Yellow Rose Yellow 791 723.29
17 Chocolate Brown 1331 1,217.07
18 Mist White 2425 2,217.42
19 Whirlpool Blue 848 775.41
20 Alfalfa Green 990 905.26
21 Ruby Red 1269 1,160.37
22 Verde Green 1441 1,317.65
23 Sky White 2269 2,074.77
24 Black Black 1496 1,367.94
25 Whirlpool Blue 815 745.24
26 Black Black 1570 1,435.61
27 Mist White 1999 1,827.89
28 Alfalfa Green 1217 1,112.82
29 Jade Green 737 673.91
30 Yellow Rose Yellow 1063 972.01
31 Cream White 1799 1,645.01
32 Black Black 2721 2,488.08
33 Ruby Red 575 525.78
34 Mist White 2305 2,107.69
35 Yellow Rose Yellow 828 757.12
36 Black Black 2037 1,862.63
37 Sky White 2157 1,972.36
38 Periwinkle Purple 1363 1,246.33
39 Coriander White 2179 1,992.48
40 Black Black 1846 1,687.98
41 Yellow Rose Yellow 1290 1,179.58
42 Black Black 1894 1,731.87
43 Periwinkle Purple 973 889.71
44 Black Black 2393 2,188.16
45 Black Black 2476 2,264.05
46 Mist White 2428 2,220.16
47 Coriander White 2488 2,275.03
48 Cream White 2379 2,175.36
49 Verde Green 600 548.64
50 Black Black 1720 1,572.77
51 Daffodil Yellow 1160 1,060.70
52 Chocolate Brown 1264 1,155.80
53 Regal Purple 1441 1,317.65
54 Daffodil Yellow 915 836.68
55 Coriander White 839 767.18
56 Black Black 1468 1,342.34
57 Black Black 831 759.87
58 Lynx Brown 936 855.88
59 Periwinkle Purple 854 780.90
60 Daffodil Yellow 1250 1,143.00
61 Coriander White 1352 1,236.27
62 Verde Green 1163 1,063.45
63 Lynx Brown 1329 1,215.24
64 Alfalfa Green 1176 1,075.33
65 Cream White 703 642.82
66 Daffodil Yellow 836 764.44
67 Periwinkle Purple 1468 1,342.34
68 Cream White 742 678.48
69 Black Black 1305 1,193.29
70 Cream White 1254 1,146.66
71 Cream White 703 642.82
72 Coriander White 774 707.75
73 Mist White 701 640.99
74 Verde Green 589 538.58
75 Black Black 697 637.34
76 Blush Red 1113 1,017.73
77 Opal Blue 732 669.34
78 Daffodil Yellow 1393 1,273.76
79 Mist White 1496 1,367.94
80 Alfalfa Green 1440 1,316.74
81 Jade Green 987 902.51
82 Verde Green 1197 1,094.54
83 Cream White 585 534.92
84 Black Black 1488 1,360.63
85 Chocolate Brown 914 835.76
86 Regal Purple 852 779.07
87 Sky White 922 843.08
88 Regal Purple 1339 1,224.38
89 Yellow Rose Yellow 1311 1,198.78
90 Lynx Brown 739 675.74
91 Regal Purple 731 668.43
92 Ash Blue 1485 1,357.88
93 Periwinkle Purple 827 756.21
94 Black Black 992 907.08
95 Black Black 581 531.27
96 Blush Red 708 647.40
97 Regal Purple 1152 1,053.39
98 Whirlpool Blue 1434 1,311.25
99 Yellow Rose Yellow 1133 1,036.02
100 Sapphire Blue 734 671.17
101 Chocolate Brown 1221 1,116.48
102 Toffee Brown 906 828.45
103 Sapphire Blue 1423 1,301.19
104 Whirlpool Blue 1287 1,176.83
105 Black Black 1277 1,167.69
106 Regal Purple 541 494.69
107 Opal Blue 501 458.11
108 Blush Red 1104 1,009.50
109 Coriander White 1187 1,085.39
110 Whirlpool Blue 1408 1,287.48
111 Ash Blue 820 749.81
112 Blush Red 1427 1,304.85
113 Black Black 517 472.74
114 Ruby Red 1279 1,169.52
115 Mist White 788 720.55
116 Chocolate Brown 508 464.52
117 Opal Blue 1267 1,158.54
118 Toffee Brown 832 760.78
119 Sky White 981 897.03
120 White White 1056 965.61
121 Black Black 1145 1,046.99
122 Chocolate Brown 1254 1,146.66
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 ooutput: What is the F value?
8) What is the F critical value?
9) What is your decision?
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?
20)
Sheet1
