In a Phase II clinical trial with a binary endpoint, 8 out of 20 patients responded...

In a Phase II clinical trial with a binary endpoint, 8 out of 20 patients responded to a new drug. Let X be the total number of patients responding to the new drug among the 20 patients and pi be the population response rate. Please specify the distribution of X and obtain a 95% confidence interval for pi.

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Expert Solution

Solution :

Given that,

Point estimate = sample proportion = = x / n = 8 / 20 = 0.4

1 - = 1 - 0.4 = 0.6

Z/2 = 1.96

Margin of error = E = Z / 2 * $\sqrt$ (( * (1 - )) / n)

= 1.96 * ( $\sqrt$ ((0.4 * 0.6) / 20)

= 0.215

A 95% confidence interval for population proportion p is ,

- E < < + E

0.4 - 0.215 < < 0.4 + 0.215

0.185 < < 0.615

The 95% confidence interval for the population proportion is : 0.185 , 0.615

orchestra answered 1 year ago

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