Question

You want to obtain a sample to estimate a population proportion.
Based on previous evidence, you believe the population proportion
is approximately p∗=23%p∗=23%. You would like to be 95% confident
that your estimate is within 3% 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.

Answer #1

Solution :

Given that,

= 0.23

1 - = 1 - 0.23 = 0.77

margin of error = E = 3% = 0.03

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_{/2}
= Z_{0.025} = 1.96 ( Using z table )

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

= (1.96 / 0.03)^{2} * 0.23 * 0.77

= 756

Sample size = 756

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