The Grocery Manufacturers Association of America found that 76% of
consumers purchased products with an "organic" label on them. The FDA –
the Food and Drug Administration – sought to confirm this finding with its
own study of n = 256 consumers. This study found that x = 160 consumers
claimed that they purchase organic products.
[Q#1] What proportion, p , of consumers purchase organic products?
(a) 25% (b) 32.5% (c) 37.5% (d) 50% (e) 62.5%
[Q#2] What proportion, q , of consumers do NOT purchase organic products?
(a) 25% (c) 37.5% (e) 62.5%
(b) 32.5% (d) 50%
[Q#3] Given the sample size, n = 256, what is the standard deviation value for
the estimated proportion for purchasing organic products, σp = ?
(a) 1.96% (c) 4.24% (e) 5.93%
(b) 3.03% (d) 5.00%
[Q#4] What is the Z-score used to construct a Margin of Error for a
95% Confidence Interval, Zα/2= ?
(a) 2.576 (c) 1.96 (e) 1.50
(b) 2.326 (d) 1.645
[Q#5] What is the Margin of Error = E for this 95% Confidence Interval?
(a) 1.96% (c) 4.24% (e) 5.93%
(b) 3.03% (d) 5.00%
[Q#6] What is the 95% Confidence Interval for the sample proportion, p ?
(a) 56.6% < p < 68.4% (c) 52.6% < p < 73.4%
(b) 54.3% < p < 70.9% (d) 50.8% < p < 76.2%
[Q#7] Using the answers from the preceding questions, what value for the
sample size = n would be needed to achieve a Margin of Error, E = .04 = 4% ?
(a) 256 (b) 400 (c) 492 (d) 563 (e) 688