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In the planning stage, a sample proportion is estimated as pˆ = 81/90 = 0.90. Use this information to compute the minimum sample size n required to estimate p with 95% confidence if the desired margin of error E = 0.08. What happens to n if you decide to estimate p with 90% confidence?

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Answer:

In the planning stage, a sample proportion is estimated as formula = 81/90 = 0.90. Use this information to compute the minimum sample size n required to estimate p with 90% confidence if the desired margin of error E = 0.08. What happens to n if you decide to estimate p with 90% confidence?

Confidence level

90% = ?

p=0.8

Z value at 90% =2.576

d=0.08

Sample size = (z2*p*(1-p))/d2

= (2.5762^2 * 0.9 * 0.2)/0.122^2

=1.19443968/0.0149

=80.16

The sample size required= 80.

90% = ?

Z value at 90% =1.645

d=0.12

Sample size = (z2*p*(1-p))/d2

= (1.6452*0.8*0.2)/0.122

=30.06

The sample size required= 31

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