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# Sample Size, Margin of error

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I) Find the minimum sample size you should use to assure that your estimate of p will be within the required margin of error around the population p.
1) margin of error:0.01; confidence level:95%; from a prior study p is estimated by the decimal equivalent of 55%.

2) Margin of error: 0.007; confidence level: 98%; p and q unknown

II) Find the margin of error : 95% confidence level interval; n =91; x (sample mean)= 85, s= 3.7

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Find the minimum sample size you should use to assure that your estimate of p will be within the required margin of error around the population p.

1) margin of error:0.01; confidence level:95%; from a prior study p is estimated by the decimal equivalent of 55%.

Sample size (proportions):

confidence interval= 95%
proportion =p= Known = 0.55
Error= ±z*sp= 0.01 or 1%
where sp=standard error of proportion=square root of (pq/n)
Thus we have to ensure that Z* sp < 1%
Z corresponding to a confidence level of 95.% and two tails = 1.9600
(from the tables or using EXCEL function NORMSINV)
Thus, sp < 1.%/Z
or sp < ...

#### Solution Summary

Calculates sample size and margin of error given confidence interval.

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