18- Genetically modified food you wish to estimate, with 99% confidence the popu

Question

18- Genetically modified food you wish to estimate, with 99% confidence the population proportion of US adults who think that food containing genetically modified ingredient should be labeled .your estimate must be accurate within 2% of the population proportion.

(A) No preliminary estimates is available. Find the minimum sample size needed.

(B) find the minimum sample size needed , using a prior study that found that 87% of US adults think THAT food containing genetically modified ingredient should be labeled. (C) compare the results from part (a )and (b).

Explanation / Answer

Question in probability & statistic

R. The equation to calculate the minimum sample size needed is:

……… (1)

Where:

n: Sample size

p: The point estimate for p, the population proportion of successes,

q: The point estimate for q, the population proportion of failure,

E: the margin of error.

Z: Statistics value that depends of confidence level.

Analysis

In this case it is assumed that p and q are equal to 0.5. This is made in this way, because assumed this values we guaranteed that these values yield the maximum value of the product p*q = p*(1-q). In other words, without an estimate of p, we should use a larger sample.

Then:

p=q=0.5

E = 0.02

Z (99% confidence level) table to normal probability distribution  

www. mat.uda.clhsalinas/sursos/2012/eyp1/tablas.pdf

1- = 0.99

= 0.01

/2 = 0.005

Z/ 2 = Z + 0.005

P(Z Z 0.005) =0.995 + (1-/2)

Z(0.99)=2.575

Substituting in equation 1.

The minimum sample size needed n = 4144

Part b)

We have p= 0.87 and q= 0.13, Z = 2.575 (99% confidence level) E = 0.02

Substituting in equation 1.

The minimum sample size with p= 0.87

n= 1875

Part c)

Interpretation:

With no preliminary estimate, the minimum sample size should be at least 4144 US adults. With a preliminary estimate of p = 0.87, the sample size should be at least 1875 US adults. So, we will need a larger sample size when no preliminary estimate is available.

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