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Health experts recommend that runners drink 4 ounces of water every 15 minutes they run. Although handled bottles work well for many types of runs, all-day cross-country runs require hip-mounted or over-the-shoulder hydration systems. In addition to carrying more water, hip-mounted or over-the-shoulder hydration systems offer more storage space for food and extra clothing. As the capacity increases, however, the weight and cost of these larger-capacity systems also increase. The following data show the weight (ounces) and the price for 26 hip-mounted or over-the-shoulder hydration systems (Trial Runner Gear Guide 2003).
Model
Weight (oz.)
Price ($)
Fastdraw
3
10
Fastdraw Plus
4
12
Fitness
5
Access
7
20
Access Plus
8
25
Solo
9
Serenade
35
Solitaire
11
Gemini
21
45
Shadow
15
40
SipStream
18
60
Express
30
Lightning
Elite
14
Extender
16
65
Stinger
GelFlask Belt
DelDraw
1
GelFlask Clip-on Holster
2
GelFlask Holster SS
Strider (W)
Walkabout (W)
Solitude I.C.E.
Getaway I.C.E.
19
55
Profile I.C.E.
50
Traverse I.C.E.
13
a. Use these data to develop an estimated regression equation that could be used to predict the price of a hydration system given its weight.
b. Test the significance of the relationship at the 0.05 level of significance.
c. Did the estimated regression equation provide a good fit? Explain.
d. Assume that the estimated regression equation developed in part (a) will also apply to hydration systems produced by other companies. Develop a 95% confidence interval estimate of the price for all hydration systems that weigh 10 ounces.
e. Assume that the estimated regression equation developed in part (a) will also apply to hydration systems produced by other companies. Develop a 95% prediction interval estimate of the price for the Back Draft system produced by Eastern Mountain Sports. The Back Draft System weighs 10 ounces.
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