Question

In a clinical trial, 50 patients who received a new medication are randomly selected. It was found that 10 of them suffered serious side effects from this new medication. let p denote the population proportion of patients suffered serious side effects from this new medication. The 90% confidence interval for p is about

Answer 1

Solution :

Given that,

n = 50

x = 10

Point estimate = sample proportion = = x / n = 10 / 50=0.2

1 -   = 1-0.2 =0.8

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z0.05 = 1.645 ( Using z table )

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

= 1.645 *((0.2*0.8) /50 )

E = 0.093

A 90% confidence interval p is ,

- E < p < + E

0.2-0.093 < p < 0.2+0.093

0.107< p < 0.293