Question

In: Statistics and Probability

Scatterplot of daily cycling distances and type of climb: Every summer, the touring company America by...

Scatterplot of daily cycling distances and type of climb: Every summer, the touring company America by Bicycle conducts the “Cross Country Challenge,” a 7-week bicycle journey across the United States from San Francisco, California, to Portsmouth, New Hampshire. At some point during the trip, the exhausted cyclists usually start to complain that the organizers are purposely planning for days with lots of hill and mountain climbing to coincide with longer distances. The tour staff counter that no relation exists between climbs and mileage and that the route is organized based on practical issues, such as the location of towns in which riders can stay. The organizers who planned the route (these are the company owners who are not on the tour) say that they actually tried to reduce the mileage on the days with the worst climbs. Here are the approximate daily mileages and climbs (in vertical feet), as estimated from one rider’s bicycle computer.

Mileage

Climb

Mileage

Climb

Mileage

Climb

83

600

69

2500

102

2600

57

600

63

5100

103

1000

51

2000

66

4200

80

1000

76

8500

96

900

72

900

51

4600

124

600

68

900

91

800

104

600

107

1900

73

1000

52

1300

105

4000

55

2000

85

600

90

1600

72

2500

64

300

87

1100

108

3900

65

300

94

4000

118

300

108

4200

64

1500

65

1800

97

3500

84

1500

76

4100

91

3500

70

1500

66

1200

82

4500

80

5200

97

3200

77

1000

63

5200

92

3900

53

2500

  1. Construct a scatterplot of the cycling data, putting mileage on the x-axis. Be sure to label everything and include a title.
  2. We haven’t yet learned to calculate inferential statistics on these data, so we can’t estimate what’s really going on, but do you think that the amount of vertical climb is related to a day’s mileage? If yes, explain the relation in your own words. If no, explain why you think there is no relation.
  3. It turns out that inferential statistics do not support the existence of a relation between these variables and that the staff seems to be the most accurate in their appraisal. Why do you think the cyclists and organizers are wrong in opposite directions? What does this say about people’s biases and the need for data

Solutions

Expert Solution

From the above scatterplot we can observe that the points in the graph are randomly scattered. There is no pattern observed here. For any mileage most of the climb fall below 2000 feet, for example a mileage of 73 has a climb height of 1000 and again a mileage of 103 has a climb height of 1000. Again a mileage of 73 has highest climb height of 8500 feet.So the pattern is random that is we cannot predict the climb height as a function of mileage. We cannot fit any relation between mileage and climb height. The pattern is random because a mileage corresponding to low distance can have low climb height again it may have high climb height.

The prediction of cyclist may be wrong due to their instance schedule. There is lots of travel day after day.So after few days they may be exhausted and conclude that higher mileage has higher climb height. On the other hand organizers claim is wrong due to the fact that they predicted the climb height wrong, the roads may be spiral and has lots of turns. So for a low climb height the cyclist has to travel more distance. So there is exist people's bias and so we need for actual data and inferential statistics to conclude the actual relationship.


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