Question

Construct a 99% confidence interval for p subscript 1 minus p subscript 2, given x subscript 1 equals 51 comma space n subscript 1 equals 150 comma space x subscript 2 equals 45 comma space and space n subscript 2 equals 180.

Answer 1

p̂1 = 51 / 150 = 0.34
p̂2 = 45 / 180 = 0.25

p̂ is the pooled estimate of the proportion P
p̂ = ( x1 + x2) / ( n1 + n2)
p̂ = ( 51 + 45 ) / ( 150 + 180 )
p̂ = 0.2909

Margin of error = Z/2 * sqrt [ p̂ ( 1 - p̂) * ( 1 / n1 + 1/ n2) ]

= 2.5758 * sqrt [ 0.2909 ( 1 - 0.2909 ) * ( 1 / 150 + 1 / 180) ]

= 0.129

99% confidence interval is

(p̂1 - p̂2) - E < p1 - p2 < (p̂1 - p̂2) + E

(0.34 - 0.25) - 0.129 < p1 - p2 < (0.34 - 0.25) + 0.129

-0.039 < p1 - p2 < 0.219

99% C I is ( -0.039 , 0.219 )