researchers have reported that the incidence rate of cataracts may be elevated a

Question

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 expected incidence rate of catarcats among 65-to 69-year olds is 1% over a 1 year period. Complete one sample binomial test, exact method and report a p-value (two-sided).

Explanation / Answer

Answer to the question)

Hypothesis:

Null hypothesis: P = 0.01

Alternate hypothesis: P 0.01

.

Sample Size n = 200

Sample proportion p^ = 4 /200 = 0.02

.

Standard error (SE) = sqrt(p * (1-p) / n)

SE = sqrt( 0.01*0.99/200)

SE = 0.0070

.

The formula of Z is :

Z = ( p^ - P) / SE

z = (0.02 -0.01) / 0.0070

z = 1.43

.

P value = 2 * (1 - 0.9236)

P value = 0.1528

.

Inference: Since the P value 0.1528 > alpha 0.05 , we fail to reject the null hypothesis

Conclusion: Thus we conclude that the incidence rate is 1% only

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