A computer dating service typically asks for various pieces of information such as height, weight, and income. One such service requested the length of index fingers. The only plausible reason for this request is to act as a proxy on height. Women have often complained that men lie about their heights. If there is a strong relationship between heights and index fingers, the information can be used to "correct" false claims about heights. To test the relationship between the two variables, researchers gathered the heights and lengths of index fingers (in centimeters) of 121 students.
a. Graph the relationship between the two variables.
b. Is there sufficient evidence to infer that height and length of index fingers are linearly related?
c. Predict with 95% confidence that height of someone whose index finger is 6.5 cm long. Is this prediction likely to be useful? Explain
|
Height (cm)
|
Index finger length (cm)
|
Gender
|
|
154.9
|
5.8
|
0
|
|
154.9
|
6.1
|
0
|
|
154.9
|
6.1
|
0
|
|
154.9
|
6.8
|
0
|
|
154.9
|
6.9
|
0
|
|
154.9
|
7.2
|
0
|
|
155.0
|
6.3
|
0
|
|
155.0
|
6.6
|
0
|
|
155.0
|
7.3
|
0
|
|
156.2
|
6.0
|
0
|
|
157.5
|
4.8
|
0
|
|
157.5
|
6.6
|
0
|
|
157.5
|
6.7
|
0
|
|
157.5
|
6.7
|
0
|
|
160.0
|
6.4
|
0
|
|
160.0
|
6.4
|
0
|
|
160.0
|
6.5
|
0
|
|
161.3
|
7.1
|
0
|
|
162.6
|
6.0
|
0
|
|
162.6
|
6.1
|
0
|
|
162.6
|
6.5
|
0
|
|
162.6
|
6.8
|
0
|
|
162.6
|
7.0
|
0
|
|
162.6
|
7.0
|
0
|
|
162.6
|
7.4
|
0
|
|
162.6
|
7.5
|
0
|
|
163.0
|
6.6
|
0
|
|
163.5
|
6.7
|
0
|
|
163.8
|
6.4
|
0
|
|
165.0
|
7.2
|
0
|
|
165.1
|
5.0
|
0
|
|
165.1
|
6.4
|
0
|
|
165.1
|
6.6
|
0
|
|
165.1
|
6.8
|
0
|
|
165.1
|
7.1
|
0
|
|
165.1
|
7.5
|
0
|
|
165.1
|
8.0
|
1
|
|
165.1
|
8.3
|
0
|
|
166.0
|
6.9
|
0
|
|
166.4
|
7.0
|
0
|
|
166.4
|
7.0
|
1
|
|
166.4
|
7.4
|
0
|
|
167.6
|
6.4
|
1
|
|
167.6
|
6.5
|
0
|
|
167.6
|
7.3
|
0
|
|
167.6
|
7.5
|
0
|
|
167.6
|
7.6
|
0
|
|
167.6
|
8.5
|
0
|
|
168.4
|
6.5
|
1
|
|
168.9
|
6.8
|
1
|
|
170.0
|
7.9
|
1
|
|
170.2
|
5.8
|
1
|
|
170.2
|
7.1
|
1
|
|
170.2
|
7.5
|
1
|
|
170.2
|
7.5
|
1
|
|
170.3
|
7.8
|
0
|
|
171.5
|
7.5
|
1
|
|
172.1
|
7.6
|
1
|
|
172.7
|
7.3
|
0
|
|
172.7
|
7.5
|
1
|
|
172.7
|
7.9
|
1
|
|
172.7
|
8.2
|
1
|
|
172.7
|
9.0
|
0
|
|
173.0
|
7.2
|
1
|
|
174.5
|
7.7
|
1
|
|
174.6
|
7.4
|
1
|
|
175.3
|
6.6
|
0
|
|
175.3
|
7.0
|
1
|
|
175.3
|
7.0
|
1
|
|
175.3
|
7.1
|
0
|
|
175.3
|
7.2
|
1
|
|
175.3
|
7.5
|
1
|
|
175.3
|
7.5
|
1
|
|
175.3
|
7.6
|
1
|
|
175.3
|
8.0
|
1
|
|
175.3
|
8.1
|
1
|
|
176.4
|
7.6
|
1
|
|
176.5
|
6.4
|
1
|
|
176.5
|
7.0
|
1
|
|
176.5
|
7.1
|
1
|
|
177.8
|
6.8
|
1
|
|
177.8
|
7.4
|
1
|
|
177.8
|
7.8
|
0
|
|
177.8
|
8.1
|
1
|
|
177.8
|
8.2
|
1
|
|
178.2
|
7.6
|
1
|
|
179.1
|
7.0
|
1
|
|
179.1
|
7.5
|
0
|
|
179.1
|
7.6
|
1
|
|
180.0
|
7.9
|
1
|
|
180.1
|
8.5
|
1
|
|
180.3
|
5.7
|
1
|
|
180.3
|
7.1
|
0
|
|
180.3
|
7.1
|
1
|
|
180.3
|
7.5
|
1
|
|
180.3
|
7.8
|
1
|
|
180.3
|
7.8
|
1
|
|
180.3
|
7.9
|
1
|
|
180.3
|
9.0
|
1
|
|
180.4
|
8.4
|
1
|
|
181.7
|
8.3
|
1
|
|
181.8
|
7.8
|
1
|
|
181.9
|
7.6
|
1
|
|
182.9
|
6.9
|
1
|
|
182.9
|
7.0
|
1
|
|
182.9
|
7.5
|
1
|
|
182.9
|
9.0
|
1
|
|
185.0
|
7.9
|
1
|
|
185.4
|
7.1
|
1
|
|
185.4
|
7.3
|
1
|
|
185.4
|
7.6
|
1
|
|
185.4
|
8.0
|
1
|
|
185.4
|
8.3
|
1
|
|
186.7
|
7.3
|
1
|
|
187.5
|
8.0
|
1
|
|
188.0
|
7.1
|
1
|
|
188.0
|
8.5
|
1
|
|
188.3
|
8.3
|
1
|
|
190.5
|
7.5
|
1
|
|
191.0
|
8.2
|
1
|
|
191.4
|
8.0
|
1
|