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In a clinical trial of oxycodone, 16 subjects experience headaches among the 227 subjects treated with oxycodone. Construct a 95% confidence interval for the proportion of treated subjects who experience headaches. Provide both probabilistic and practical interpretations. (Hint: this is proportion problem).

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Answer:

95% Confidence Interval = (0.037, 0.104)

Step-by-step explanation:

The formula for Confidence Interval if a proportion is:

p ± z × √p(1 - p)/n

z = z score of a 95% confidence interval = 1.96

p = proportion = x/n

x = 16, n = 227

p = 16/227

p = 0.0704845815

≈ 0.0705

Confidence Interval

= 0.0705 ± 1.96 × √0.0705(1 - 0.0705)/227

= 0.0705 ± 1.96 × √0.0002886773

= 0.0705 ± 0.0333013921

Confidence Interval

= 0.0705 - 0.0333013921

= 0.0371986079

≈ 0.037

= 0.0705 + 0.0333013921

= 0.1038013921

≈ 0.104

Hence, 95% Confidence Interval = (0.037, 0.104)

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