Use the given data to find the minimum sample size reqired t

Use the given data to find the minimum sample size reqired to estimate a population proportion or percentage.

1) Margin of error: eight percentage points; confidence level 95%; from a prior study, p is estimated by the decimal equivalent of 52%

n= ______ ( Round uo to the nearest integer )

2) Many states are carefully considering steps that would help them collect sales taxes on items purchased through the internet. How many randomly selected sales transactions must be surveyed to determine the percentage that transpired over the internet? Assume that we want to be 99% confident that the sample percentage is within four percentage points of the true population percentage for all sales transactions.

n=_________ ( Round up to nearest integer )

Solution

(1) Given a=1-0.95=0.05, Z(0.025) = 1.96 (from standard normal table)

So n=(Z/E)^2*p*(1-p)

=(1.96/0.08)^2*0.52*(1-0.52)

=149.8224

Take n=150

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(2) Given a=1-0.99=0.01, Z(0.005) = 2.58 (from standard normal table)

We use p=0.5 as estimated.

So n=(Z/E)^2*p*(1-p)

=(2.58/0.04)^2*0.5*(1-0.5)

=1040.062

Take n=1041