Question

The proportion of people who relapse at twelve months posttreatment for heroin addiction is 0.75.is 0.75.

Suppose that researchers at a treatment facility use simple random samples to ensure that this number is not changing. Determine the value of ^pp^ such that in 99%99% of all simple random samples of size n=50n=50, the proportion of people in the sample who relapse at twelve months posttreatment for heroin addiction is less than ^p.than p^.

You make find a z-tablez-table or some software manuals useful.

Please give your answer to two decimal places.

Answer 1

Solution

Given that,

p = 0.75

1 - p = 1 - 0.75 = 0.25

n = 50

= p = 0.75

=  [p( 1 - p ) / n] = [(0.75 * 0.25) / 50 ] = 0.0612

Using standard normal table,

P(Z < z) = 99%

= P(Z < z ) = 0.99

= P(Z < 2.33 ) = 0.99  

z = 2.33

Using z-score formula,

= z *   +  

= 2.33 * 0.0612 + 0.75

= 0.89