Question

You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately p ∗ = 39 % . You would like to be 90% confident that your estimate is within 2% of the true population proportion. How large of a sample size is required?

How would I get this and where can I find a correct chart to base my z-table numbers off of to help me solve this easier?

Answer #1

Solution :

Given that,

= 0.39

1 - = 1 - 0.39 = 0.61

margin of error = E = 2% = 0.02

At 90% confidence level z

= 1 - 90%

= 1 - 0.90 =0.10

/2
= 0.05

Z/2
= Z_{0.05 = 1.645 ( using standard normal z
table)}

Sample size = n = (Z_{/2}
/ E)^{2} *
* (1 -
)

= (1.645 / 0.02)^{2} * 0.39 * 0.61

=1609

Sample size = 1609

You want to obtain a sample to estimate a population proportion.
Based on previous evidence, you believe the population proportion
is approximately p*=39%p*=39%. You would like to be 99% confident
that you estimate is within 2.5% of the true population proportion.
How large of a sample size is required?
n =
Do not round mid-calculation. However, use a critical value
accurate to three decimal places.

You want to obtain a sample to estimate a population proportion.
Based on previous evidence, you believe the population proportion
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within 2% of the true population proportion. How large of a sample
size is required?
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