Question

Construct a confidence Interval for p₁- p₂, at a 95% level of confidence, if x₁= 366, n₁=535, x₂=435, n₂=593

Answer 1

Solution :

Given that,

n1 = 535

x1 = 366

= x1 / n1 = 366 / 535 = 0.684

1 - = 1 - 0.684 = 0.316

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.960

Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 1.960 * (((0.684 * 0.316) / 535) = 0.039

A 90 % confidence interval for population proportion p1 is ,

- E < P1 < + E

0.684 - 0.039 < p < 0.684 + 0.039

0.645 < p < 0.723

The 95% confidence interval for the population proportion p1 is : ( 0.645 , 0.723)

Given that,

n2 = 593

x 2 = 435

= x / n = 435 / 593 =0.734

1 - = 1 - 0734. = 0.266

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.960

Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 1.960 * (((0.734 * 0.266) / 593) = 0.036

A 95 % confidence interval for population proportion p2 is ,

- E < P2 < + E

0.734 - 0.036 < p < 0.734 + 0.036

0.698 < p2 < 0.770

The 95% confidence interval for the population proportion p2 is : ( 0.698 , 0.770)