SOLUTION: After sampling from two binomial populations, we found the following: p = 0.48 n1 = 100 p2 = 0.052 n2 =100 if we estimate with 90% confidence the difference in population pro

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Question 333318: After sampling from two binomial populations, we found the following:
p = 0.48 n1 = 100 p2 = 0.052 n2 =100
if we estimate with 90% confidence the difference in population proportions, what would be the outome?

Answer by jrfrunner(365) About Me  (Show Source):
You can put this solution on YOUR website!
you can apply the binomial method directly which can be tedious and difficult
or "if" the assumptions are met, can apply a normal approximation to the binomial.
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The enable the use of the normal approximation, the following need to be met
1. n%5B1%5D%2Ap%5B1%5D%3E5 and n%5B2%5D%2Ap%5B2%5D%3E5 and n%5B1%5D%2A%281-p%5B1%5D%29%3E5 and n%5B2%5D%2A%281-p%5B2%5D%29%3E5
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you provided p1 = 0.48 n1 = 100 p2 = 0.052 n2 =100
NOTE: not sure if your p2 is correct. Nevertheless, it looks like the requirements above are met.
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90% confidence interval for difference in the population proportions yields Z=1.645
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Upper confidence interval value:
Lower confidence interval value:
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confidence interval = %280.48-0.052%29-1.645%2Asqrt%280.48%2A0.52%2F100%2B0.052%2A0.948%2F100%29 to %280.48-0.052%29%2B1.645%2Asqrt%280.48%2A0.52%2F100%2B0.052%2A0.948%2F100%29
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you can do the math