Question

A. Determine the sample size required to estimate a population proportion to within 0.034 with 93.2% confidence, assuming that you have no knowledge of the approximate value of the sample proportion.

Sample Size =

B. Repeat part the previous problem, but now with the knowledge that the population proportion is approximately 0.3.

Answer #1

Solution:

Given that,

A ) = 0.5

1 - = 1 - 0.5 = 0.5

margin of error = E = 0.034

At 93.2% confidence level the z is ,

= 1 - 93.2% = 1 - 0.932 = 0.068

/ 2 = 0.068 / 2 = 0.034

Z_{/2} = Z_{0.034} =
1.825

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

= (1.825 / 0.034)^{2} * 0.5 * 0.5

= 720.38

n = sample size = 720

B ) = 0.3

1 - = 1 - 0.3 = 0.7

margin of error = E = 0.034

At 93.2% confidence level the z is ,

= 1 - 93.2% = 1 - 0.932 = 0.068

/ 2 = 0.068 / 2 = 0.034

Z_{/2} = Z_{0.034} =
1.825

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

= (1.825 / 0.034)^{2} * 0.3 * 0.7

= 605.08

n = sample size = 605

Determine the sample size necessary to estimate a population
proportion to within 0.02 with 98% confidence assuming that
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population proportion.
You have some idea about the population proportion and believe
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confidence, when a previous study has shown
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a) 95% confidence.
b) 99% confidence.

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