Solve the following problem:
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
|
12
|
|
Access
|
7
|
20
|
|
Access Plus
|
8
|
25
|
|
Solo
|
9
|
25
|
|
Serenade
|
9
|
35
|
|
Solitaire
|
11
|
35
|
|
Gemini
|
21
|
45
|
|
Shadow
|
15
|
40
|
|
SipStream
|
18
|
60
|
|
Express
|
9
|
30
|
|
Lightning
|
12
|
40
|
|
Elite
|
14
|
60
|
|
Extender
|
16
|
65
|
|
Stinger
|
16
|
65
|
|
GelFlask Belt
|
3
|
20
|
|
DelDraw
|
1
|
7
|
|
GelFlask Clip-on Holster
|
2
|
10
|
|
GelFlask Holster SS
|
1
|
10
|
|
Strider (W)
|
8
|
30
|
|
Walkabout (W)
|
14
|
40
|
|
Solitude I.C.E.
|
9
|
35
|
|
Getaway I.C.E.
|
19
|
55
|
|
Profile I.C.E.
|
14
|
50
|
|
Traverse I.C.E.
|
13
|
60
|
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.