SOLUTION: Assume that a sample is used to estimate a population proportion (p). Find the Margin of Error (E) that corresponds to the given statistics and confidence level. Round the margin o

Question 1128508: Assume that a sample is used to estimate a population proportion (p). Find the Margin of Error (E) that corresponds to the given statistics and confidence level. Round the margin of error 4 decimal places.
90% confidence, n= 300, x=140
I attempted to find p by dividing x/n and got 0.4666667, ad used that to get 1 which i got 0.54 from but when i did the equation it gave me 0.09xxxx which is not even close to the answers I had to choose from :(.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

At 90% confidence, the critical z value is approximately 1.645

How to get this critical value? By looking up a table of values such as this one. For that specific table, look at the bottom row that starts with z. Right above the "90% confidence level" we see the value 1.645, which means that 90% of the area is between -1.645 and 1.645 under the normal curve. A table such as the one mentioned should be found in your book (likely the appendix). You can also opt to use a calculator to compute the critical z value through the use of the invNorm function on TI83 and TI84 calculators.

With z = 1.645, we can find the margin of error E using the formula below
E = z*sqrt(phat*(1-phat)/n)
where
phat = x/n = 140/300 = 0.4666667

So,
E = z*sqrt(phat*(1-phat)/n)
E = 1.645*sqrt(0.4666667*(1-0.4666667)/300)
E = 0.04738141553989
E = 0.0474

Answer: 0.0474

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