Table 1 is a data dictionary for a hypothetical study which assesses the association between the need of corrective lenses and several factors. Download the dataset eye.dta(data is at the end) from the Canvas. The outcome variable is lenses, to indicate if the participants require corrective lenses by the time they are 30 years old. Assume all participants do not need them at a baseline assessment when they were 10 years old and none of them have had serious head injuries or had brain tumors during the 20 years between assessments. The variable carrot indicates whether a participant have a gene which causes one to have a lifelong love and craving for carrots (Suppose each subject was screened for this gene at baseline). Other variables include gender and latitude (what latitude of the continental US they lived on the longest).

Table 1.

Variable name	Label	Values
ID	Participant's ID
Lenses	Whether require corrective lenses when reach 30 years old	0 = No 1 = Yes
Carrot	Gene which causes long-life craving for carrot	0 = Not have this gene 1 = have this gene
Gender	Gender	0 = Male 1 = Female
Latitude	The latitude of the continental US they lived on the longest

Based on the study description and the data provided above, run the appropriate analysis and answer below

Among those who have the carrot-craving gene, what is the "risk" (proportion) of requiring corrective lenses?

Among those who do NOT have the carrot-craving gene, what is the "risk" (proportion) of requiring corrective lenses?

What is the difference in the "risk" of requiring corrective lenses between those with carrot-craving genes and those without?

Suppose you want to use the risk ratio to compare the risk ("proportions") of requiring corrective lenses between those who have the carrot-craving gene and those who do not. What's your null hypothesis and what is your alternative hypothesis for the value of the risk ratio?

What is the risk ratio (relative risk) of requiring corrective lenses for those with carrot-craving genes compared to those without? How would you interpret the 95% CI for the risk ratio?

Based on your result in the above, do you think the risk ratio significantly differs from the null value using a significance level of=0.05? What's your conclusion?

id	carrot	gender	latitude	lenses
1	0	0	33	1
2	0	1	46	1
3	1	0	32	1
4	0	1	26	0
5	1	0	25	1
6	1	1	48	0
7	0	0	39	1
8	0	1	24	0
9	0	0	35	0
10	0	0	42	1
11	1	0	35	0
12	0	1	44	0
13	1	0	35	1
14	1	0	25	0
15	1	0	24	0
16	1	0	38	0
17	1	0	28	1
18	0	0	43	0
19	1	0	44	0
20	0	0	46	1
21	0	0	37	1
22	0	1	33	0
23	0	1	42	1
24	1	1	31	1
25	0	1	46	1
26	0	0	32	1
27	0	1	30	0
28	0	1	27	1
29	1	0	45	0
30	1	0	39	0
31	0	1	47	1
32	1	0	39	0
33	1	0	48	1
34	0	0	47	0
35	0	0	32	0
36	0	0	31	0
37	1	1	26	1
38	0	1	28	1
39	0	0	25	1
40	1	1	25	0
41	1	0	31	0
42	1	1	47	1
43	1	0	32	1
44	1	1	24	1
45	1	1	37	0
46	1	1	26	0
47	0	1	41	1
48	0	1	43	1
49	0	0	45	1
50	0	0	27	1
51	1	0	31	0
52	0	1	40	0
53	0	1	37	0
54	1	1	48	0
55	0	1	26	0
56	0	1	33	1
57	0	0	48	1
58	1	1	24	1
59	0	0	32	1
60	1	0	40	1
61	0	1	45	0
62	1	0	40	0
63	0	0	36	1
64	0	1	42	0
65	1	1	44	0
66	0	0	44	1
67	1	1	47	0
68	1	1	27	1
69	1	0	33	1
70	0	0	29	1
71	0	0	42	0
72	1	0	40	0
73	0	1	44	1
74	1	1	41	0
75	1	1	26	1
76	1	1	27	0
77	0	1	29	1
78	0	0	33	1
79	1	1	31	1
80	1	1	33	0
81	1	0	43	1
82	1	1	33	1
83	0	1	43	1
84	0	0	39	1
85	1	1	47	0
86	1	0	46	1
87	1	1	27	0
88	1	1	38	0
89	1	0	34	0
90	1	0	40	0
91	1	0	27	1
92	0	0	29	1
93	1	0	43	1
94	0	0	40	0
95	1	0	31	0
96	1	1	38	0
97	0	1	30	1
98	1	1	26	0
99	0	0	43	1
100	0	1	33	1