Question
State
Average Beer Consumption in 2010 (measured in gallons)
Average Teacher Salary in 2010 (measured in $)
ALABAMA
21.9
40347
ALASKA
19.8
53553
ARIZONA
22.0
44672
ARKANSAS
19.1
42786
CALIFORNIA
18.4
59825
COLORADO
22.0
44439
CONNECTICUT
16.2
59304
DELAWARE
25.4
54264
FLORIDA
21.0
43302
GEORGIA
18.4
48300
HAWAII
22.4
49292
IDAHO
20.1
41150
ILLINOIS
21.4
58686
INDIANA
19.1
47255
IOWA
25.4
41083
KANSAS
20.5
41467
KENTUCKY
17.9
42592
LOUISIANA
24.7
40029
MAINE
24.2
40737
MARYLAND
17.4
54333
MASSACHUSETTS
19.5
56369
MICHIGAN
19.8
54739
MINNESOTA
20.6
48489
MISSISSIPPI
24.2
40576
MISSOURI
23.1
40462
MONTANA
30.5
39832
NEBRASKA
25.2
40382
NEVADA
26.8
44426
NEW HAMPSHIRE
32.7
45263
NEW JERSEY
16.8
58156
NEW MEXICO
23.7
41637
NEW YORK
16.5
57354
NORTH CAROLINA
19.9
43922
NORTH DAKOTA
29.8
37764
OHIO
22.5
50314
OKLAHOMA
20.4
38772
OREGON
22.7
50044
PENNSYLVANIA
21.7
54027
RHODE ISLAND
20.0
54730
SOUTH CAROLINA
24.2
43011
SOUTH DAKOTA
27.5
34709
TENNESSEE
19.0
42537
TEXAS
23.9
41744
UTAH
12.4
40007
VERMONT
26.2
46622
VIRGINIA
20.1
43823
WASHINGTON
19.1
46326
WEST VIRGINIA
23.0
38284
WISCONSIN
26.3
46390
WYOMING
24.4
43255
a.
Use STATDISK to determine if there is there linear correlation between the per capita beer consumption and average teacher’s salary at a 99.5% confidence level.
Is there linear correlation?
b.
Explain your answer to Question #3. You may want to indicate your r-value and critical r-value in your explanation.
Note that a 99.5% confidence would be 0.995, so the significance would be 0.005.
c.
Use these results to explain, in your own words, the statement “Correlation does not imply causality.”
Make sure you’re using the results, so you should use beer drinking and teacher salaries to explain the statement.
..ooo Verizon 11:51 PM Done 1 of 4 VILLAGE BEDS Realigning Sales Territories oe Flicker was the newly hired national sales manageable first step. The problem was ho manager for Village Beds. It was his first day draw the boundary lines. Village Beds had l on the job and he was a bit overwhelmed by used states as control units, and he saw no t e had to do One significant problem, however, not to continue doing that. umped out at him as a high prionity: His new com- puny's sales territories were seriously out of balance reaction to any realignment plan. Many of the sal and realignment was long overdue Flicker was concerned about his people had close ties to certain customers A relatively small company in the health care they would hate to leave behind. Also, it was ineni equipment industry. Village Beds, manufactured a table that he would reduce the territory size foe line of beds especially designed for nursing homes. some. He was especially worried about the Village Reds was started just 20 years ago in Toedo. from Max Harris, who had sold village Beds in the Ohio, by its current president, Steve Moser Before Midwest territory for over 15 years. The Midkes the company, Moser had been a nursing not only had potential that far exceeded any me administrator for more than 20 years. This territory, it was also the berritory in which v Beds was best known given its Ohio headquares gave him insight into the many problems that both ts and staff had with standard nursing home He developed his new line of beds with these Harris also happened to be a close of Steve Moser, the company personal friend president. problems in mind. Although expensive, Village Flicker had a spreadsheet file com for durability, quality, and value taining the have an excellent reputation in the industry various statistics for each state or control unit (see Table 13-1B). He sat down at his computer and however, was not an expert at design- began the task of realigning territories, He wanted to do it right. His goal was to create 10 teritories ing a sales and marketing team. The initial sales territories were developed arbitrarily and were that were as equal as possible with regard to changed only by necessity as Village Beds grew potential and workload. In addition, he wanted t minimize the changes to the existing territories in and hired more salespeople. Currently, the com y pany has a sales force of just seven salepeogi e, order to keep the current seven salespeople happy who call directly on nursing home companies across the United States. Compensation, which is a combination salary plus commission, varies QUESTIONS: greatly across the seven salespeople 1. What is the best way to realign the existing seven territories into 10 new territories? (Use including key statistics for the seven sales termifa spreadsheet is strongly advised tones and reps. The sales territories were clearly 2·Should the current seven salespeople be Table 13-1A outlines the current situation, including key statistics for the seven sales terri- out of balance. Not only could Lee Flicker quickly consulted for the realignment plan? Or discern this from looking at the statistics, but he had already heard complaints During his first should the new territories be created withou their input? phone call to her, Mary Jones, sales rep in the cen 3. To which of the new territories should Max tral district, had told him that the inequity of the Harris and the other current salespeople be sales territories was causing morale problems for her and others. Flicker already had a lead on three experienced salespeople he could hire. He decided that moving from 7 to 10 territories was a logical, assigned? To which of the new territocies should the three new reps be assigned? Explain your reasoning. 394
Explanation / Answer
(a) Sample size, n:50 and Degrees of freedom:48
Correlation Results:
Correlation coeff, r: -0.4321384
Critical r: ±0.3909297
P-value (two-tailed): 0.00173
Regression Results:
Y= b0 + b1x:
Y Intercept, b0: 33.68097
Slope, b1: -0.0002528
Total Variation: 728.5392
Explained Variation: 136.0501
Unexplained Variation: 592.4891
Standard Error: 3.513335
Coeff of Det, R^2: 0.1867436
(b) There is a weak correlation since r = -0.4321 which is a low value
(c) r = -0.4321 and critical r for a significant correlation = 0.3909
(d) r is negative here.This proves that correlation does not imply causation. Higher salaries are associated with lower beer consumption which is against the expectation that higher salaries should be associated with higher beer consumption.
Hope this will be helpful. Thnaks and God Bless You :-)
