Question

If a previous study found that 29% of adults purchase used items instead of new ones, how large would your random sample need to be to perform a follow up study to confirm your initial findings (note that you want to be within 0.089 of the actual population proportion with 90% confidence)?

Answer 1

Solution :

Given that,

= 0.29

1 - = 1 - 0.29 = 0.71

margin of error = E =0.089

At 90% confidence level z

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z0.05 = 1.645 ( Using z table ( see the 0.05 value in standard normal (z) table corresponding z value is 1.645 )   

Sample size = n = (Z/2 / E)2 * * (1 - )

= (1.645 / 0.089)2 * 0.29 * 0.71

=70.34

Sample size = 70