A Research and Development Laboratory researcher for a paint company is measuring the level of a certain chemical contained in a certain type of paint.If the paint contains too much of this chemical,the quality of the paint will be compromised.How many cans of paint should the sample contain if the researcher wants to be 95% certain of being within 1% of the true proportion of this chemical?
A)9604
B)1107
C)26
D)645
E)5936

Question

Quizplus · Accepted Answer

To achieve 95% certainty within 1% of the true proportion, the sample size formula for proportions can be used: $n = \frac{Z^2 \cdot p \cdot (1-p)}{E^2}$, where $Z$ is the Z-score for the desired confidence level (1.96 for 95%), $p$ is the estimated proportion (0.5 used for maximum sample size), and $E$ is the margin of error (0.01 for 1%). Plugging in the values: $n = \frac{(1.96)^2 \cdot 0.5 \cdot (1-0.5)}{(0.01)^2} = 9604$.

A Research and Development Laboratory Researcher for a Paint Company