A concessionaire that provides services at a baseball stadium must know what siz
ID: 3354678 • Letter: A
Question
A concessionaire that provides services at a baseball stadium must know what size crowd is expected during the coming week in order to know how much food, etc., to order. Since advanced ticket sales give an indication of expected attendance, food needs might be predicted on the basis of the advanced sales. In an attempt to do such a prediction, the number of hot dogs sold per week and the advanced ticket sales for a random sample of 21 weeks (for which there were baseball games) was selected. The data is given below (in thousands):
Week Hot Dogs Sold Ticket Sales
1 36.7 32.3
2 12.0 9.5
3 27.6 23.6
4 18.9 14.8
5 18.4 10.1
6 36.8 26.4
7 31.3 20.2
8 16.8 16.5
9 24.6 22.3
10 40.0 26.3
11 17.3 14.8
12 32.5 25.5
13 21.6 14.8
14 25.8 21.2
15 34.0 25.3
16 16.8 15.3
17 29.6 30.1
18 13.9 14.1
19 28.1 27.5
20 21.2 18.2
21 24.6 18.2
Prepare a typed report with appropriate analyses incorporated that address the following questions of the concessionaire:
a. Can advanced ticket sales be used to predict hot dog sales?
b. In general how strong is the connection between hot dog sales and advanced ticket sales?
c. If so, with reasonable certainty how many hot dogs should be ordered for each of the next 3 weeks which have advanced ticket sales of 21,600, 17,400, and 44,000 respectively?
d. The average number of advanced ticket sales per week for the entire year is 23,000. With some degree of certainly, how many hot dogs would be sold per week on the average, if advanced ticket sales were 23,000 per week?
Explanation / Answer
.a. Can advanced ticket sales be used to predict hot dog sales?
The regression equation is
Sold = 23.2 + 0.0632 Sales
Predictor Coef SE Coef T P
Constant 23.158 1.915 12.09 0.000
Sales 0.06324 0.03106 2.04 0.056
S = 7.51978 R-Sq = 17.9% R-Sq(adj) = 13.6%
Ans: Advanced ticket sales cannot be used to predict hot dog sales at 0.05 level of significance whereas it may be in 0.10 level of significance the advanced ticket sales have a significant effect on hot dog sales at 0.10 level of significance.
b. In general how strong is the connection between hot dog sales and advanced ticket sales?
Ans: In general the relation is a medium connection between hot dog sales and advanced ticket sales because the correlation value is 0.423.
c. If so, with reasonable certainty how many hot dogs should be ordered for each of the next 3 weeks which have advanced ticket sales of 21,600, 17,400, and 44,000 respectively?
Ans: i) advanced ticket sales = 21,600
Sold = 23.2 + 0.0632 *21600=1388.32
ii) advanced ticket sales = 17,400
Sold = 23.2 + 0.0632 *17400=1122.88
iii) advanced ticket sales = 44,000
Sold = 23.2 + 0.0632 *44000=2804
d. The average number of advanced ticket sales per week for the entire year is 23,000. With some degree of certainly, how many hot dogs would be sold per week on the average, if advanced ticket sales were 23,000 per week?
Ans: Sold = 23.2 + 0.0632 *23000=1476.8
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