Question

In: Statistics and Probability

The research firm LL Research collected data from 200 client businesses. They want to determine how...

The research firm LL Research collected data from 200 client businesses. They want to determine how the businesses compare among four variables:

2015 Profit in millions of dollars
2016 Profit in millions of dollars
2015-2016 Two-Year Change in Daily Average Customer Visits

Two-Year Average Number of Employees

Data collected for the sample of 200 businesses is contained in the file named Businesses, linked at the bottom of the page. Use all 200 data points.

Managerial Report
Prepare a report (see below) using the numerical methods of descriptive statistics presented in this module to learn how each of the variables contributes to the success of a client business. Be sure to include the following three items in your report.

1. Find descriptive sample statistics (mean, median, two quartiles Q1 and Q3, minimum, maximum, range, sample standard deviation, and coefficient of variation) for each of the four variables along with an explanation of what the descriptive statistics tell us about the client businesses.

2. Compute the percent change in profit from 2015 to 2016 for each business. Then use the z-score to determine which businesses were outliers with respect to percent change in profit.

3. Compute the sample correlation coefficient, showing the relationship between percent change in profit and each of the other two variables (2015-2016 Two-Year Change in Daily Average Customer Visits and Two-Year Average Number of Employees). Explain what the correlation coefficients tell us about the three pairs of relationships. Use tables, charts, or graphs to support your conclusions.

Number Business 2015 Profit 2016 Profit Two Year avg. change in daily no. of visits Two Year Average Number of Employees
1 B Phillips 4436 8108 37 100
2 Barr & Edwin Co. 7452 9542 82 71
3 Lacrosse Archery 2564 2125 6 41
4 Global Fleet Sales 4547 5219 40 56
5 ALLSTATE ATHLETIC SUPPLY 8028 6160 85 79
6 ELECTROPOWER UTILITY SALES 1313 5074 -7 31
7 Bergner's 6843 7211 71 97
8 BESLEY'S 4280 7775 34 54
9 Dave Ranney & Assoc 4721 9674 40 89
10 RDI Technologies 3603 4881 17 37
11 Rocky MTN HMO - Info. & Sales 2701 7172 7 63
12 Mid-South Sweeper Supply; Inc 3119 8327 12 85
13 WestLake Supply 4308 6516 36 43
14 Old Town Artisans Galleries 4550 2305 40 48
15 Client Services Guy 5267 8804 46 32
16 Bill Reed 8973 4747 93 86
17 Game Fair Ltd 7366 2629 80 96
18 Air Supply Systems; Inc 5905 7186 54 38
19 The Webmaster 3701 9466 20 44
20 First Supply Group; Inc 1180 7572 -8 26
21 Comfyco 6980 930 73 95
22 Telson; Inc 2117 2414 4 66
23 One Plus Two 1219 1108 -8 83
24 FlowTech Supply 2817 5635 9 91
25 Brewer Business Supply 3142 2651 14 44
26 King Plaza-Management Lsng 2533 3784 6 47
27 Sales Recruiting Specialist 7021 9522 75 62
28 Lenty Sales; Inc. 1654 1841 -3 21
29 Vipbrasil 7713 6069 83 74
30 Empire State Sales Inc 6244 1063 57 26
31 Sunday Sales 8838 2851 91 26
32 Spa City Silver 5777 3058 51 24
33 Cps 4504 6606 39 65
34 WSA Sales Co. Inc 1990 6252 -2 65
35 Sun State Sales 6541 5904 67 58
36 KWICK SUPPLY INC 4541 8953 39 67
37 Power Solutions Inc 5662 5125 50 71
38 Reece & Nichols Wyandotte 9286 1158 94 42
39 Harmony Ball 5414 2769 48 98
40 Eagle Flight Safety Products 5505 4364 49 66
41 Team Vehicle Sales 3444 4977 14 50
42 Papaya Clothing 3703 4059 20 39
43 Daniels & Fry Motor Company 5009 3286 44 29
44 Home Base Solutions 8229 9303 87 50
45 SAFsystems 4800 4999 42 69
46 Robert Rytter & Associates 8424 3258 89 79
47 Arbor Consulting 6488 1039 62 30
48 DEANGELO MACHINERY SALES 6287 5524 58 44
49 JDG Sales And Service 3844 7146 25 74
50 MOSS 6730 8194 71 72
51 Sonya C. Atwell 5695 7747 51 47
52 Sentry Network Service; Inc. 3579 6245 17 39
53 SUMMIT FINANCIAL GROUP 1737 2498 -3 57
54 Lenexa Office Supply 7001 4820 74 35
55 Cyberzone 6699 8272 69 38
56 Monarch Rep Sales Inc 8868 6316 92 21
57 Eddiechamberland 7114 7116 76 63
58 EXCEL PRODUCTS 5239 7248 45 70
59 Samco Sales 6541 2355 67 49
60 Lajobi Sales; Inc 4484 4466 38 74
61 ECS Anchor Supply 8655 3577 91 100
62 Tiger Sales 4278 7425 32 39
63 Auto Graphics Sales 9678 2829 97 39
64 Algin Technology LLC 4440 3301 38 51
65 Triple T Sales 3687 6882 19 89
66 Georges Miret Salon 8906 1063 93 35
67 NICHOLSON; WILLIAM 2991 3746 11 66
68 Sears Grand 992 8233 -10 57
69 Active Fitness And Aerobics 4106 9366 29 93
70 Crosstech 3527 9840 16 69
71 Druglaunch 8190 5866 86 58
72 Brian Sullivan Enterprises 6966 1888 72 56
73 PC SALES 9268 6999 94 77
74 Starr Gennett Foundation 6132 9766 55 62
75 KCI Sales 8134 9845 85 60
76 Mapleshade Lane E 2595 962 6 26
77 Rod Dow 3136 5738 14 95
78 CC Industrial Sales 4301 9571 36 20
79 Southwest Distributing; Inc. 5513 7564 49 54
80 Robert M. Wells 1541 2515 -5 83
81 United Sales & Services; Inc 8249 4299 88 25
82 NO. Power Plant 6137 5846 55 54
83 BREWARES INC 9936 5651 100 32
84 Closeouts Attic 6720 8230 69 40
85 AGEE Sales; Inc. 6253 8833 57 80
86 Jason Golden 5564 5855 50 94
87 Shepherd Sales 2178 6106 4 22
88 John C Weigand 6376 8755 60 32
89 Discount Silks 7664 9634 83 48
90 Ban-Koe Systems Inc. 5335 1975 47 96
91 Shamrock Computer 9843 7688 89 55
92 Margaret Lucas 2500 1800 12 79
93 Shafer Valve 5939 2399 32 99
94 RTG INDUSTRIAL SUPPLY; INC 6135 3000 44 84
95 American Supply Group 9567 7654 72 95
96 Mr. Spindle 300 500 -8 45
97 Jones Services Supply Co. 4455 2342 23 55
98 Factory Direct Craft Supply 5671 2355 23 49
99 Metro Sandwiches & Salads 9937 7890 100 70
100 Global Industrial Sales 1255 1200 1 23
101 Fun Yards 2244 1289 5 66
102 Taylor Supply 8875 6040 55 33
103 Facility Robotics; Inc 1309 1268 3 34
104 Tele-Sales Consultants; Inc 2500 1321 5 67
105 Hometown Paintball Supply Inc. 9943 853 120 77
106 Bales Hay Sales 9897 7800 99 32
107 Zero systems 3467 2333 17 48
108 Agm 7686 5622 44 77
109 Simcha Sales 9000 6843 56 67
110 Pauls Motor Sales And Service 9000 9957 56 100
111 Drillers Supply 9583 1685 81 35
112 Sharper Concepts; Inc 2728 1360 7 80
113 Pat Tomek 9345 1312 43 66
114 Mbh Sales And Service 9471 3405 96 52
115 Howard Sales Co.; Inc 1488 6142 -7 23
116 SELECT SALES; INC. 3246 3549 14 24
117 John Garesche 7462 5052 82 68
118 TOP SALES COMPANY; INC 8551 3427 89 67
119 On Angels Wings 2599 2740 6 23
120 WebStar Designs 7521 7907 82 40
121 Lone Pine Sales 7937 5991 85 50
122 Associated Supply Co 9202 7112 94 95
123 John Cody 7230 4503 79 92
124 Barton Mattress Sales 6399 3312 61 71
125 InternetNow 3675 9576 19 70
126 Corrosion Guard 6536 8512 63 40
127 Comet Website Consultants 2464 4501 5 26
128 MCMAHON; JOHN 4084 5773 28 59
129 Alan Warren 1124 5168 23 83
130 ROV Supply CO 2371 4610 4 49
131 Wilrock Sales Corp 6361 7557 60 75
132 Lowe Co Motion Inc. 3509 6616 16 80
133 Daley Plastering 7675 5536 83 86
134 Walter Drake Inc 8011 2665 85 68
135 Philips Business Solutions 8417 2808 88 88
136 Bacik Karpinski Associates Inc 7190 8807 77 41
137 Jeff Munchick Sales 5499 5077 49 23
138 GEO-THERMAL SALES; INC 6720 7404 70 99
139 Sprinkler Supply Company 9686 1178 99 96
140 Rol-Tru Putting Greens 9432 2599 95 25
141 Energy Mgmt Systems 5050 6596 45 69
142 B & D Sales 7529 1033 82 55
143 Tech-Tran Corp. 6877 1271 72 52
144 Judy Rees 6459 1996 61 32
145 Jenskates 4048 3723 28 68
146 Custom Filter Supply; Inc 2110 4898 3 57
147 Fiduciary Trust Co. Intl 4429 9501 36 73
148 The Office Supply Store; Inc. 8898 8190 93 53
149 Char Sakamoto Ishii Lum Ching 6274 7326 58 85
150 Otto Wolff U.S. Sales Corp 7162 4839 76 74
151 Bailey Slipper Shop 3883 7446 26 44
152 Megaidea; Inc 5962 2154 55 49
153 Jeff Branch Motor Sales 8845 6854 92 99
154 Aeropostale Inc 4735 1110 42 31
155 High Tides 3134 5581 13 33
156 Foley's Department Store 6100 1948 55 51
157 Gornet Technologies 3615 1225 18 69
158 Brinton Vet Supply 6308 8620 59 20
159 The Jones Shop 1004 7848 -10 81
160 WOODSTOCK QUILT CO.; INC 8427 7816 89 79
161 KWB SALES 4228 2742 32 52
162 Efficient Lighting Sales Co. 7381 7066 81 37
163 Filene'S 3913 1176 27 71
164 Gemini Technical Sales 5827 1504 53 75
165 Walter Long 3714 1584 21 97
166 Cloutier Property Management 9566 6887 97 78
167 ATMCo 7180 2327 76 67
168 Mark Maggiacoma 9973 8707 101 79
169 Global Granite 7608 8684 83 39
170 NuHS 5337 2539 48 26
171 JTC Express Office Supply 6751 6204 71 81
172 Inductive Technologies; LLC 7701 9342 83 41
173 Florida Villa Vacations Inc 1917 9450 -2 77
174 Misty Mountain Sales 5012 2294 44 29
175 Outpost 6640 4570 67 72
176 Dollar All 7879 5010 83 71
177 Clinical Laboratory Standard 7546 1229 83 20
178 AdultPaths.com 9627 3445 97 79
179 Ship Supply Of Florida; Inc. 4039 1385 27 68
180 M Hoffman Enterprises Inc. 3068 2896 11 45
181 Worldscale Association 9070 7770 94 34
182 Dream Weavers Network 9401 7552 95 53
183 Mr. Trademark Inc. 3754 4761 24 90
184 Jefferson Financial 3730 5878 21 78
185 P J P Sales 7900 6278 84 81
186 Mylon C. Jacobs Supply 2911 4628 11 86
187 Terry Smith 1569 2078 -3 60
188 Smith Supply 3337 5390 14 24
189 Complete Police Supply Limited 2342 5262 4 94
190 Design Build Concepts 8181 7472 86 34
191 Bon Voyage Travel 8702 3493 91 66
192 Diverse Technologies Corporation 9537 3047 97 59
193 Magic Dollar 3503 2386 16 65
194 Syracuse Castings Sales 8596 4174 91 81
195 McCormick Sales And Service 6196 2909 56 49
196 Zecharya Sales & Services;Inc 9167 1727 94 45
197 Marinette Co. Abstract & Land 6257 3575 57 78
198 BoKip Sales 4183 1880 30 85
199 Mark's Sales 7135 6928 76 39
200 Pete Reilly Consultants 4992 5412 43 55

Solutions

Expert Solution

ANS::

given that

2015 Profit in millions of dollars
2016 Profit in millions of dollars
2015-2016 Two-Year Change in Daily Average Customer Visits

Two-Year Average Number of Employees

Data collected for the sample of 200 businesses is contained in the file named Businesses, linked at the bottom of the page. Use all 200 data points.

Managerial Report
Prepare a report (see below) using the numerical methods of descriptive statistics presented in this module to learn how each of the variables contributes to the success of a client business. Be sure to include the following three items

SOLL::::

Step 1

Analyze – descriptive statistics – frequencies

Step 2

Statistics

2015 Profit

2016 Profit

Two Year avg. change in daily no. of visits

Two Year Average Number of Employees

N

Valid

200

200

200

200

Missing

0

0

0

0

Mean

5609.14

5177.85

49.72

59.91

Median

5802.00

5101.00

51.00

62.00

Std. Deviation

2524.385

2682.574

33.177

22.625

Range

9673

9457

111

80

Minimum

300

500

-10

20

Maximum

9973

9957

101

100

Percentiles

25

3606.00

2740.50

19.00

40.00

50

5802.00

5101.00

51.00

62.00

75

7592.50

7384.50

82.00

78.75

Step 3

Coefficient of variation= ( Std. Deviation/ Mean)*100

We find the variability in 2016 profit is higher compared to 2015

Compute the percent change in profit from 2015 to 2016 for each business. Then use the z-score to determine which businesses were outliers with respect to percent change in profit.

Percent change in profit = (2016 profit – 2015 profit )/ 2015 profit

Z score= ( Percent change in profit – mean (percent change in profit ) )/ S.D (percent change in profit )

In spss ,

Go to

Analyze – descriptive statistics –descriptive

Then make sure,’ save standardized values as variables’, is ticked

The click ok

Z-score is got in data view

Findings

Outliers-

Those that are beyond 3 stdanadrd deviations are selectred as outliers

Here it is.

68-Sears Grand

102-Taylor Supply

159- The Jones Shop

Compute the sample correlation coefficient, showing the relationship between percent change in profit and each of the other two variables (2015-2016 Two-Year Change in Daily Average Customer Visits and Two-Year Average Number of Employees). Explain what the correlation coefficients tell us about the three pairs of relationships. Use tables, charts, or graphs to support your conclusions.

Correlation

To looks for

  • Statistical significance-a correlation is statistically significant if its “Sig. (2-tailed)” < 0.05.
  • Correlation coefficient

Step 1

Spss

Analyze—correlate- bivariate

Step 2

Correlations

Zscore: Percent change in profit

Two Year avg. change in daily no. of visits

Zscore: Percent change in profit

Pearson Correlation

1

-.351**

Sig. (2-tailed)

.000

N

200

200

Two Year avg. change in daily no. of visits

Pearson Correlation

-.351**

1

Sig. (2-tailed)

.000

N

200

200

**. Correlation is significant at the 0.01 level (2-tailed).

Correlations

Zscore: Percent change in profit

Two Year Average Number of Employees

Zscore: Percent change in profit

Pearson Correlation

1

.078

Sig. (2-tailed)

.272

N

200

200

Two Year Average Number of Employees

Pearson Correlation

.078

1

Sig. (2-tailed)

.272

N

200

200

Step 3

Percent change in profit and Two Year avg. change in daily no. of visits

  • Statistically significant(0.000<0.05)
  • Coefficient   =   - 0.351

Percent change in profit and Two Year Average Number of Employees

  • Not Statistically significant(0.272 > 0.05)
  • Coefficient   =   0.272

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