# Researchers have reported that

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 people, 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.

*7.49 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).

# Researchers have reported that

Researchers have reported that the incidence rate of cataracts may be elevated among people with excessive expo- sure 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.

Problem a)  What test procedure can be used to compare the
1-year rate of cataracts in this population with that in the
general population?
Problem b) Implement the test procedure in Problem a, and
report a p-value (two-sided).

# Researchers have reported that

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 people, 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.

*7.50 Construct a 95% CI for the 5-year true rate of cataracts among the excessive-sunlight-exposure group

# Researchers have reported that

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.

# Researchers have reported that

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 people, 4 develop cataracts over a 1-year period. Suppose the expected incidence rate of cataracts among 65- to 69-yearolds is 1% over a 1-year period.

A) What test procedure can be used to compare the 1-year rate of cataracts in this population with that in the general population?

B) Implement the test procedure in Problem 7.52, and report a p-value (two-sided). 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.

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