Researchers have reported that the incidence rate of cataracts may be elevated among people with excessive exposure to sunlight. To confirm this, a pilot study is conducted among 200 people ages 65–69 who report an excessive tendency to burn on exposure to sunlight. Of the 200 peo- ple, 4 develop cataracts over a 1-year period. Suppose the expected incidence rate of cataracts among 65- to 69-year- olds is 1% over a 1-year period. The researchers decide to extend the study to a 5-year period and find that 20 of the 200 people develop a cataract over a 5-year period. Suppose the expected incidence of cataracts among 65- to 69-year-olds in the general population is 5% over a 5-year period. a)Test the hypothesis that the 5-year incidence rate of cataracts is different in the excessive-sunlight-exposure group compared with the general population, and report a p-value (two-sided). b) Construct a 95% CI for the 5-year true rate of cata- racts among the excessive-sunlight-exposure group
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
Researchers have reported that the incidence rate of cataracts may be elevated among people with excessive exposure to sunlight. To confirm this, a pilot study is conducted among 200 people ages 65–69 who report an excessive tendency to burn on exposure to sunlight. Of the 200 peo-
ple, 4 develop cataracts over a 1-year period. Suppose the expected incidence rate of cataracts among 65- to 69-year- olds is 1% over a 1-year period.
The researchers decide to extend the study to a 5-year period and find that 20 of the 200 people develop a cataract over a 5-year period. Suppose the expected incidence of cataracts among 65- to 69-year-olds in the general population is 5% over a 5-year period.
a)Test the hypothesis that the 5-year incidence rate
of cataracts is different in the excessive-sunlight-exposure
group compared with the general population, and report a
p-value (two-sided).
b) Construct a 95% CI for the 5-year true rate of cata-
racts among the excessive-sunlight-exposure group.
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