Find a 90 percent confidence interval for the difference between the proportions of failures in factory 1 and factory 2 where ₁ = .05, ₂ = .04,n₁= 500,n₂ = 2000. A)(-0.0037 0.0237) B)(-0.0076 0.0276) C)(0.0004 0.0196) D)(0.0098 0.0102)

Question

Quizplus · Accepted Answer

To find the confidence interval, we can use the formula
(point estimate) ± (critical value) * (standard error)
where the point estimate is the difference in proportions (0.05 - 0.04 = 0.01), the critical value can be found using a t-distribution with degrees of freedom equal to the smaller of (n1-1) and (n2-1) (in this case, df = 498), and the standard error is calculated as
sqrt( p̂1(1 - p̂1)/n1 + p̂2(1 - p̂2)/n2 )
where p̂1 and p̂2 are the sample proportions (0.05 and 0.04, respectively).

Plugging in the numbers, we get:
point estimate = 0.01
standard error = sqrt(0.05*0.95/500 + 0.04*0.96/2000) = 0.0147
critical value for a 90% confidence interval with df = 498 is approximately 1.645

So the 90% confidence interval is:
0.01 ± 1.645*0.0147
= (-0.0076, 0.0276)

Therefore, the best choice is B, which matches this interval.

Find a 90 Percent Confidence Interval for the Difference Between