A confidence interval for the difference between the population proportions = ( .2597 , .3403 )
Confidence interval mean
Estimate's mean plus and minus the range of that estimate's fluctuation is called a confidence interval.
In statistics, a claim to 95% confidence simply means that the researcher has seen one possible interval from a large number of possible ones, from which 19 out of 20 intervals contain the true value of the parameter.
If repeat the test, can expect your estimate to fall between these numbers with a reasonable degree of certainty.
In statistics, confidence is another probability word.
β₁ = x₁/n₁ = 582/600 = 0.97
β₂ = x₂/n₂ = 268/400 = 0.67
( β₁ - β₂) ± z √β₁( 1 -β₁ )/n₁ + β₂(1 - β₂)/n₂
= (.97 - .67 ) ± 1.645 √.97( 1 - .97)/600 + .97( 1 - .67)/400
= .30 ± 0.4336
= ( .2597 , .3403 )
A confidence interval for the difference between the population proportions = ( .2597 , .3403 )
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= 8
