The critical value used for finding a 98% confidence interval is z = 2.33.

n1 = 1400, n2 = 1320

p1 = .5, p2 = .38

q1 = .5, q2 = .62

q1 is 1 - p1 and q2 is 1 - p2

The formula used for finding the confidence interval of a difference in proportions is:

CI = p1 - p2 +/- Z*sqrt((p1*q1)/n1 + (p1*q1)/n2)

We plug in our values which gives us:

98% CI = .5 - .38 +/- 2.33*sqrt((.5*.5)/1400 + (.38*.62)/1320)

=> .12 +/- 2.33*sqrt(.25/1400 + .2356/1320)

=> .12 +/- 2.33*sqrt(1.7857E-4 + 1.78485E-4)

=> .12 +/- 2.33*sqrt(3.571E-4)

=> .12 +/- 2.33*.0189

=> .12 +/- .044

98 % confidence interval = (.08, .16)

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