Question

A certain drug is used to treat​ pain, but it is dangerous because it is addictive and can be lethal. In clinical​ trials,

235

subjects were treated with the drug and

49

of them developed nausea.

a. Construct a

95​%

​(Wald) confidence interval estimate of the percentage of users of the drug who develop nausea.

Answer 1

Solution :

Given that,

n = 235

x = 49

Point estimate = sample proportion = = x / n = 49/235=0.209

1 -   = 1- 0.209 =0.791

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z _0.025 = 1.96   ( Using z table )

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

= 1.96 (((0.209*0.791) /49 )

E = 0.114

A 95% confidence interval is ,

- E < p < + E

0.209-0.114 < p < 0.209+0.114

0.095< p < 0.323