Question

A researcher for paint company is measuring the level of a certain chemical contained in a particular type of paint. If the paint contains too much of this chemical, the quality of the paint will be compromised. On average, each can of paint contains 10 percent of the chemical. How many cans of paint should the sample contain if the researcher wants to be 98 percent certain of being when 1 percent of the true proportion of this chemical?

4870

1107

26

645

Answer 1

Solution :

Given that,

= 0.10

1 - = 1 - 0.10 = 0.90

margin of error = E = 0.01

At 98% confidence level

= 1 - 98%

=1 - 0.98 =0.02

/2 = 0.01

Z/2 = 2.326

sample size = n = (Z _{/ 2} / E )² * * (1 - )

= (2.326 / 0.01)² * 0.10 * 0.90

= 4869.24

sample size = n = 4870