Question

Two samples are taken with the following numbers of successes and sample sizes t1 = 32 r2 = 24 n1 = 60 n2 = 99 Find a 99% confidence interval, round answers to the nearest thousandth. <P1 - P2 Box 1: Enter your answer as an integer or decimal number. Examples: 3,-4, 5.5172 Enter DNE for Does Not Exist, oo for Infinity Box 2: Enter your answer as an integer or decimal number. Examples: 3, 4, 5.5172 Enter DNE for Does Not Exist, oo for Infinity

Answer 1

Let r₁ = x₁ ,

r₂ = x₂

The sample proportion 1 is computed as follows, based on the sample size N = 60 and the number of favorable cases X1 = 32: X1 32 = = 0.533 99 and the number The sample proportion 2 is computed as follows, based on the sample size N, of favorable cases X = 24:

The critical value for a = 0.01 is c = 21-a/2 = 2.576. The corresponding confidence interval is computed as shown below: a - (M-in-zip Mp') 2010: P). p- *o + p 8.mi) pe )

0.533 -0.242 - 2.576 x V 0.533(1-0.533) 60 0.242(1 - 0.242) 0.533-0.242 +2.576 0.533(1 -0.533) V 0.242(1 -0.242) 99 = (0.091, 0.49)

Answer : 99% confidence interval  0.091 < p1​−p2 < 0.490