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A concession stand wants to determine, with 90% confidence, what proportion of people like lettuce on their hamburgers.They want to know the correct proportion to within 4%.A preliminary study showed that 36% of those surveyed like lettuce on hamburgers.What sample size is necessary to estimate the true proportion of people who like lettuce on their hamburgers?

Answer :

To calculate the size of the sample we use the following formula:

[tex]n=\frac{Z^2P(1-P)}{d^2}[/tex]

N is the size of the sample, P is the expected proportion of people liking lettuce (36% for this case) and d is the precision, 4% in this case. Z is the Z score for confidence. In this case, 90% of confidence will have a Z value of 1.645.

Then, applying the formula:

[tex]\begin{gathered} n=\frac{1.645^2\cdot0.36(1-0.36)}{0.04^2} \\ n=389.66 \end{gathered}[/tex]

Rounding to the unit, the sample size should be 390.

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