SOLUTION: You wish to estimate with 95% confidence the population proportion of US adults who think that the president can do alot about the gasoline. Your estimates must be accurate within

Question 977663: You wish to estimate with 95% confidence the population proportion of US adults who think that the president can do alot about the gasoline. Your estimates must be accurate within 4% of yhe population proportion. A) no preliminary estimate is available. Find the minimum sample size needed.
B) Find minimum sample size needed using. a prior study that found that 48% of Usadults think the president can do a lot about the price of gasoline. Compare the results of a and b
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
In both cases, the margin of error is E = 0.04. The critical value is approximately z = 1.96 (found using a table or calculator)

A)

"no preliminary estimate is available" so assume that p = 0.5

n = p(1-p)(z/E)^2

n = 0.5(1-0.5)(1.96/0.04)^2

n = 600.25

n = 601

Notice how I rounded up to the nearest whole number.

Min sample size needed is 601

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b)

Now we are told that p = 0.48

n = p(1-p)(z/E)^2

n = 0.48(1-0.48)(1.96/0.04)^2

n = 599.2896

n = 600

Again, round up to the nearest integer.

Min sample size needed is 600

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There isn't much difference between the two min sample sizes: 601 from part a) and 600 from part b)
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